If you are here on a Visa or have a Green Card, any time you are arrested for any crime you should get copies of everything (court records, police reports, etc.). Take the documents to an Immigration Attorney as soon as possible to know if you can fix the problem and how. Any time you travel you should have copies of these documents with you.
In regard to your new Visa, depending on the type you may have different way of applying for a new one. In many cases there are 2 steps. The 1st step is that the Employer (if this a Work Visa) submits a petition for you. After the petition is approved, you submit an Application for a Visa. However, very often, once you leave the country you cannot be admitted because of your crime and the U.S. Government usually does not tell you that when the Employer’s Petition is approved.
You can try to fix the problem while you are in your home country but it is much more difficult if not impossible in many cases. There are ways to address the problem but it is quite difficult and time consuming. It is better, faster and easier in many cases to have the problem fixed while you are here in the U.S. In conclusion, when faced with a crime don’t wait to the last minute and be caught unprepared to address the problem.
Please contact a licensed Immigration attorney before you act on your specific situation. Immigration Laws and Federal Regulations are constantly changing and the general information provided can change over time.