Tune in to how the locals speak and compare it to your way of speaking. The more you listen to them, the more you will adjust your pacing, choice of words and pronunciation.
Listen to television personalities and news announcers. They have been trained to speak in a neutral accent. Try repeating some of the things they say. It can be difficult to tell if you're progressing with your accent reduction. Ask a friend to listen to you and to point out what makes your speech different.
If you get teased about certain words, you can consciously train yourself to change that word. I moved from the midwest to the east coast, and trained myself to quit saying it's time to "warsh" the clothes. Now I say "wash," but it took awhile to correct myself.
It isn't always the way you say something, it can be your choice of words that betray that you aren't from this area. For instance, some regions say "soda" and some say "pop" and some say "cola." You need to train your ear to pick up the preferred words used by locals. After some time, you won't even think about it. When you go back to your hometown, you'll have to remember to say "supper" even though in the place you now live, it's called "dinner."
You can buy CDs or DVDs that are accent reduction programs. Check at the public library to see if they have them available for borrowing.