I am married to a foreign national, and so I've given the illegal immigration issue a lot of thought. The problem needs to be fixed in the same way that a hole in the side of your house needs to be fixed before winter.
Here is a principled approach that may anger a lot of conservatives who consider my registration idea amnesty, but nonetheless it is a practical solution.

Step1:
Secure the border. This must be done by
a. Allowing our Border Patrol to patrol the border, rather than be locked in prison for attempting to do so as has recently occurred.
b. Increasing manpower at the border. The agents are good, but we need more.
c. Increasing resources at the border. Border patrol agents need better equipment. Modern technology would allow virtual lockdown of the border, much more efficiently than simply building a fence could. For a minimal cost, we could use predator drones equipped with cameras, motion sensors, and satellite imagery to create virtual fence.
d. Use military control until a,b and c are implemented.
Border control is the necessary first step. Nothing else can work until it is implemented. Sadly, some people see border control as the only solution. Recognizing it as part of the solution rather than the only thing to fix is what would give conservatives the initiative to push it through. If set out as a part of the bigger picture I outline below, even liberals would have to admit that it isn't hate mongering.
Since we encourage legal immigration to our country, the purpose of containing the border is to control who comes, and ensure that the immigrants we don't want (criminals, drug/human traffickers, etc) can't get in. This requires massively increases of support to the border patrol in terms of manpower and technology, and inventive fixes like posting military along the border and creation of a wall. As Fred Thompson has repeatedly said, border security is primarily a national security issue, and only SECONDARILY an immigration issue.

Step 2:
Alien Registration for those here.
This is both a pragmatic and necessary step, as well as the most controversial that I propose. Pragmatic because we will not be able to forcefully remove the millions of illegals here. It will also be necessary to get any law to pass in our current political climate. It is also the right thing to do, as I will explain below.

Alien registration is to get the names and information of every illegal alien withing the borders of the United States, to conduct background checks and then put them on the road to residency. Straight amnesty increases illegal immigration since more will come if the carrot of citizenship is dangled in front of their face. That is why we secured the border back in step 1. This would prevent an influx of immigrants wanting the citizenship, as well as any future immigration. That is why it was step 1.

Those opposed to amnesty will also state that we don't want to reward people who have broken the law. In fact, the “A” word is the spark to the powderkeg in conservative circles, but it must be addressed. True, illegal aliens have flouted our immigration laws to be here, yet we share as much fault for not enforcing the law ourselves for decades. We have allowed the problem to escalate to its current form. For years, we have ignored the immigration situation. So now that we have shown how important we consider the laws by ignoring them for years, we suddenly expect illegals to consider it important? Something different than breaking laws is at work here. Its like the speed limit: a law in place that is rarely followed. But if it such a vital law, why do we all break it and expect law enforcement to ignore it? Why don't we immediately revoke driver's licenses when people break the speed limit? Aren't they blatantly breaking the laws?

How do we expect immigrants to value laws we ourselves have neglected? In fact, in a twisted way, since they don’t respect immigration laws, they have picked up on that part of American culture.

Actually, traffic and speeding laws are enforced with GREATER consistency than our immigration laws… Yet I digress...

Just like the traffic laws, when one breaks it, they are forced to pay a fine and then expected to get on the straight and narrow. Because there are a great amount of illegals here who are honest workers amidst those who are scumbags we don't want in society, we give them a chance to say "obey the law or leave." We do this by requiring a massive registration. This will be staged process.

The first stage will be to impose a 3 month deadline for all illegals to register at their local INS. Through successive stages, they will then be required to prove that they have a clean background, they have a working level of English, they have employment and are not a public burden, etc., with the final stage being able to gain a permanent residency status. Citizenship would be reserved for those who return to their home country and apply in their turn. The total process would take perhaps a decade. Each stage would have an application fee paid by the immigrant to pay for the expenses of verifying this information. Any immigrant who does not register, who does not pass the stages, or who fails to complete a stage is deported. This will not encourage more illegal immigration, because those who do not register within the 3 month window will be unable to apply. Will it create a surge on the border during the months leading up to the passing of this law and the registration period? Yes. But it is better to bleed and then stop the flow than to bleed until you die.

Doing this will allow the honest workers and families to stay, while cleansing our country of the drug dealers, welfare leeches, and those who will not strive to gain citizenship. We live in a society that can create our own laws to reflect our values. Is this a case where the laws should be changed instead of enforced?

Just like a traffic ticket, we require a fee, a show of lawful behavior. It is a fair, just solution that will stand up to any amount of liberal counter-arguments.

Step 3:
Decrease incentive to be here illegally.
We need to decrease the incentive for those here illegally to be here after the registration is through.

Police will be allowed to question residency status, or as the case may be, the stage of registration that the immigrant is in.

Employers who pay illegal immigrants “under-the-table” will be subject to a similar fine the IRS has in place for tax evaders: an anonymous tip system with rewards. The catch is, even the illegal immigrant can be rewarded with a monetary donation for reporting an employer. The penalty must be exacted on the businessman who attempts to hire illegals. While a few illegals may gain money this way, it will quickly dry up the market for illegal labor. Who would work for $2 per hour when you can get $10,000 for making a phone call?

In order to be fair to the businessman, a database will be made available for employers to cross-check the social security number and name of employees. If the name and number don’t match, the employer cannot deduct that salary from taxes, and they must pay a penalty.

Contrary to liberal assertions, this is not a violation of privacy, since employers don’t need to know whose numbers are whose, only that the information claimed by the employee is or is not a “match.”

Step 4:
Increase visas. In order to invite my wife's brothers (who are minors) on a simple tourist
visa, we have to pay a fee in order to make an appointment to submit the
application at the embassy. We set up the appointment and were informed that we
would have to wait 6 months for our application to even be submitted. Notice that
a six month wait isn't to be approved, rather the six months is simply to
have the privilege of submitting a piece of paper. That is ridiculous. The condition for immigrant visas is even worse. When we were considering petitioning her mother for an immigrant visa, we found out that the expected wait in order to be approved is 14 years. That is unacceptable. In all practicality, we have illegal immigration in this country because people CAN’T come here legally, despite the rhetoric that "we aren't against immigration, merely illegal immigration."

14 years is too long. It is massive red-tape bureaucracy. We need to fix that. All costs to accelerate the process could be subsidized by those applying. From application to visa shouldn't take more than one year. We screen for the drug dealers and criminals, everyone else gets a shot to come and begin the immigration process. Part of the application process is to prove financial independence, either through the immigrant or a sponsor, so avoiding welfare leeches will be ensured even with an increase in visas. The requirements for visas should be a background check for criminal activity and a means of support once here, as well as continued monitoring of that status once in the country.

Step 5:
Decrease demand on immigration. People will want to come to America. That will always be a fact until every country is free. But why is there no push to build a border fence to keep out the Canadians? The reality of the current immigration problem stems from South American (and that mostly Mexican) immigrants. That is the flow we need to slow down to a manageable level. Why would someone want to leave their family for years, to go to a distant land where they don't even speak the language to clean restrooms at Walmart? Only if you want to deal heroin or if the country you come from is so horrible that you cannot survive there. If you could make more money in one week of work than you could in an entire year in your own country, and your family was in abject poverty, would you risk coming to a land where they don’t even speak English to provide for them?

So, we use all of America's influence through bribery, political pressure, sanctioning, etc. to give economic incentives to those countries so that people can get jobs in their own country. We offer micro-loan programs to developing countries, we offer help in maintaining law and order and cleaning up corruption, we offer aid in establishing schools to train people to work in their own country. Expensive? Yes, but cheaper than the amount we currently spend on illegals.

As well as incentives for other countries, we need penalties for those who don’t comply. For example, our military can claim one acre of land and 100 barrels of oil for every illegal Mexican immigrant caught after the registration period. We cut the ability to send money to foreign countries from foreign workers. The full weight of American embargoes and political pressure can be brought to help other countries understand and agree to follow mutually beneficial policies.