What is the best strategy for tutoring peers?

Mr. Bonaparte's advice is awesome!
You can also offer to do the work together, and when they struggle, offer to show them how you did it, step by step. Be humble, speak about the way you do the work not that it is easy for you, like "this way helped me" or "here is another way to do this".

When working with peers, the best way I've found to offer help is by not offering it...first. When other students are struggling they know it, and often those who are open to help will voice it. However, it's not always as simple as someone coming up to you and saying "Can you help me with this?" Sometimes that happens, but more often than not it will be in the form of an indirect ask or signal. Phrases such as "This topic is so confusing," or "I don't get this at all and my teacher is really bad at explaining it," or "Maybe I should get a tutor, because there's no way I'm going to pass this class." These types of statements are prime opportunities for you to offer help.

By asking (and not telling) if you could help in a way that is genuine and focused on helping them and not proving your skills, most people will be very receptive and appreciative. Saying something along the lines of "If it would help, I can show you some of the strategies that helped me to understand the material," comes off a lot better than "This stuff is really easy for me, let me help you get it." The first one is focused on helping them to understand using their own skills, while the second is focused on how good you are at this particular topic. The first statement will work a lot better than the latter.

Some of your classmates may respond negatively, but that's out of your control, and based on feelings that they have about inferiority and proving themselves or other internal challenges. There's nothing you can do about that, and I wouldn't take it personally.

It's great that you want to help others, and don't feel that you need to tread too lightly, just be sure to look for signals before you reach out.