Ok. You need to retrieve your military records from the archives first.
Once you have that information, you need to file a DD Form 293 with the discharge upgrade board appropriate for your branch of service. The appropriate location to file that form is actually found on the form (each branch is listed). You can find the form online.
You do not need an attorney to file that request, however, the percentages show that individuals that use an attorney to help formulate and organize their application for upgrade have better success. You can find plenty of attorneys that do this work simply by typing attorney and DD Form 293 in google.
Now, I want to warn you in advance that the process is slow and not as successful as most servicemen were perhaps led to believe it would be when they separated. It is actually not a common occurrence for these things to be upgraded. Less than 1/3 of General discharges are ever upgraded to Honorable.
The applications that have the best chance of gaining the upgrade contain two things.
1. Evidence of positive life changes since the separation to include education, community connection and service, etc.
2. Applications demonstrate how the General Discharge is hindering them from fully engaging in the positive life changes they've already mentioned. It's holding them from higher education or more important jobs, etc.