Approaching teachers to ask them for a letter of recommendation can be a tough thing to do. It made me very nervous as well, so you're definitely not alone in feeling awkward about it. Luckily, you'll only need about 1 or 2 for college admissions. As far as "tips or tricks" in doing this, there is really no better way than simply walking up to their desk before/after class (if they don't seem too busy) and politely asking them for a letter of recommendation for college or whatever the case may be.
What can make the process easier, however, is asking teachers that you are most comfortable with. Bonus points if you did/are doing well in that teacher's class or have a good relationship with him/her. It doesn't necessarily have to be a teacher that you currently have. When I asked for my letters, I asked one of my sophomore-year teachers that I had a very good relationship with. I really respected this teacher and I felt that the feeling was mutual, so I did not feel awkward at all in asking this teacher for a letter of recommendation. Ideally, you want to ask a teacher that knows you well, so that they have more personal subjects about you to highlight. Like I said earlier, bonus points to you if you did well in the class also because your work ethic and intelligence will be other factors that the teacher can bring up about you.
Make a list of the top 3-4 teachers you would like to ask for a letter of recommendation and ask them nicely outside of class time. Teachers are there to help you grow as a student, so they will be very happy to help you out. Also, they will be flattered that you chose him/her over the many other teachers at school! The worst thing that could happen is that they will say they are too busy with other work. In that case, just thank them for their time and move on to the next teacher!
It just starts with one question! Best of luck to you with this and with getting good letters of recommendation!