Once an immigrant has been removed (deported) from the United States, federal immigration laws make it very difficult to return. In most cases, the immigrant 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 immigrant 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 immigrant 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 U.S. legally. Unfortunately, the legal terminology is quite technical. We'll give you a brief rundown here, but analyzing the law and applying it to your own situation will require an attorney's help.
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'll need to present convincing and sympathetic reasons why the waiver should be granted.
If you've 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'll need help from someone who is knowledgeable and experienced.