Note: I am of course assuming that it was not an intentional violatiom because why would you read this if so. I'm also writing this in the context of a relationship but it mostly applies to casual encounters as well.
If someone lets you know that you have violated their sexual consent, here's how I suggest you react:
1) Listen carefully and accept their experience as real without editing or "interpreting.".
Do not reframe what they say as "you did bad" or "I'm mad at you" -- instead listen for each specific action you took which caused them pain. You need this information in order to keep from violating people in the future.
2) Apologize in very plain words and use the language they used.
If they called it rape, call it rape; if they called it sexual violation, call it sexual violation. Don't make it sound worse or better than they did. Do not assume you can guess the impact; don't assume it is devastating and don't assume it is NOT devastating.
3) Do not request or expect any kind of response.
Accept that they may never respond. Accept that they have the right to be angry or sad. Do not ask for nor expect forgiveness. This is not about you.
4) Do not use negative language about yourself and do not talk to them more than once about your guilt / sadness / etc about your mistake.
DO NOT SEEK COMFORT FROM THEM. DO NOT make them defend you by whining about how you feel like a terrible person. Find someone else to talk to about it. Seriously. Don't make your feelings their problem.
5) Figure out why you did what you did, and be very honest with yourself; then IF they ask why, tell them.
Don't shy away from uncomfortable truths like "I cared more about getting sexual gratification than I cared about how my actions might affect them" or "I didn't bother to think about their boundaries or desires." If your reason was terrible, you must accept and admit it or all hope is lost of you not violating someone like that again. also, don't tell them why unless they confirm that they want to know: telling them may cause additional pain so it MUST be their choice.
6) Figure out how you can prevent yourself from making the same mistake.
Then in extremely brief words, IF they are trying to rebuild with you, describe how you will prevent this happening again. no more than one long sentence. don't make them listen to your whole damn life plan.
7) Ask what, if anything, you can do to best help them recover from the violation and be determined to do anything you can.
Offer 2-3 things with a wide range between so that they can tell you really mean it and know how far you are willing to go. Don't offer anything you can't do.
For example, "if you need to change our relationship to nonsexual for a time or forever, I am okay with that; if you need to be out of contact for a time or forever, I can support that; if you need me to give you nonsexual physical affection every day, I will do that as long as I can. Or if you think of anything you'd like me to do please let me know."
Make sure you are clear that they can ask for anything, and you will do what is within your resources to do. If you don't want to do everything that is within your resources to do, have the decency to end the relationship. Violating someone sexually will not be healed with anything less than whole-hearted efforts.
8) do what they ask without bargaining or complaint.
If they want to heal without you, accept that and move on. Do not keep offering things after they said no. Do not try to bargain! Do not try to change what they asked for. If you're not sure what they mean, ask clarifying questions like "this or that?" and phrase them in neutral ways.
9) Don't ask for new kinds of relationship or household work from them for a while.
If this situation made you realize some new thing you want from them, keep that to yourself unless specifically asked, and wait until they seem to be less fragile to discuss it. This is not the time to be asking for emotional labor -- or any labor -- from them.
10) Don't try to have sex with them again unless and until they tell you that they would like that.
Let them know that you are not going to initiate sex unless / until they express a desire for that. Don't bring it up. don't hint. don't make sly comments or "jokes." If they decide they do want to have sex with you, trust that they know themself and accept their desire as real. Be very alert to their feelings the entire time and ask questions before increasing the intensity.
11) if you tend to avoid and suppress emotion, learn to express in an ethical way. Do the work!
If your reason for violating them had anything to do with avoiding or suppressing your emotions, and you have the ability to do so, then do SOME kind of intensive, continuous work to learn how to process your emotions: go to therapy or take a class or complete a workbook etc. Keep going until you start getting spontaneous compliments on your emotional maturity.
Handling your own emotions is a basic necessity of being an adult and if you are so bad at it that you violated someone sexually because of it, your need to learn is at emergency status. DO NOT ASK THE PERSON YOU VIOLATED TO HELP YOU. Not even if they are a therapist. Not even if they're really good at it. Be careful not to put the burden of your inexperience on them.