You either have a bad ignition switch, a short somewhere, or you need a new starter. If I had to guess I'd say a new starter. You need to bypass the "start" part of the ignition switch by directly jumpering the starter, (if you don't know how to do that, I'd say take it somewhere), the starter will engage, then if you remove the jumper, the starter should disengage and stop. If it doesn't, you need a starter (or a rebuild), if it does, there is a problem in your ignition switch. Good Luck.
There are two possibilities. The solenoid is integral to starter. That's probably where the problem is.
But the problem could be at the ignition key.
How to test? If the key "feels weird", like it is not returning from start position, that's a hint.
You'll be down there or your mechanic will be down there to replace starter. The first thing one does is to remove wires. Test wires to see a wire lights up a test light with key in 'Start " position and goes off when you release key. If not, leave starter in place and look to ignition switch.