Only few Thais can master Thai tones perfectly. Most of them can speak but cannot spell correctly.

This mastering of Thai tones must be the most challenging task for you.

Local Thai

Since tone is embedded in every Thai word you will have some serious leaks in your Thai if you don't hammer them early and build the foundation. Though it does depend on how far you would like to take your Thai.

As far as learning them, look up on Youtube "Stu Jay Raj" he has some great in-depth videos on how to form these sounds correctly. You'll want to use a lot of mimicking early on, find a few different Thai people and audio programs and mimic them nonstop until it feels more comfortable. This is a skill and it takes time to build. Start with single words slowly then move on to sentences. Notice their flow in sentences and try to copy that over and over.

For a few months,many years ago, I had a few cds in the car and continually played them all the time I was driving. When the opportunity arose I would try to use what I had picked up.

Never been backward in coming forward I had no problem or anxiety in using by new words and phrases and found Thai's very helpful in correcting my mistakes. To my regret never learned to read or write, but I can at least get by fairly well with the spoken word so I guess the tones came with it.