Once a foreign national has been removed (deported) from the United States, federal immigration laws make it very difficult to return. In most cases, the person becomes what's called "inadmissible," and must spend several years outside the United States before a return is legally allowed.
This is true even if the foreign national might normally be granted an immigrant visa or green card, for example through marriage to a U.S. citizen. There is some hope in this particular case, however. The foreign national might be able to apply for a waiver of admissibility, allowing early return and receipt of an immigrant visa or green card (lawful permanent residence).
After having been removed from the United States, the inadmissibility laws set varying amounts of time during which the person will be barred from reentering the United States legally. Unfortunately, the legal terminology is quite technical. We will give you a brief rundown here, but analyzing the law and applying it to your own situation will require an attorney's help.
For example:
If you are married to a U.S. citizen, then you are considered an "immediate relative" under the family categories found within U.S. immigration laws. That means that, in theory at least, you can apply for an immigrant visa (green card).
However, anyone can be denied a green card if found inadmissible. So, as part of your application, you'll need to apply for a waiver of inadmissibility. Such a waiver is available in most of the situations described above. But you will need to present convincing and sympathetic reasons for why the waiver should be granted to you.
If you have been removed or deported from the United States and have any thoughts of returning, consult with an immigration attorney first. In fact, look for an attorney with a sub-specialty in reentry after removal, who both understands the laws and has succeeded with past waiver requests. This is a tricky area of the law, and you will need help from someone who is knowledgeable and experienced.