Karate-do Gi and Obi
Your karate uniform is known as your do-gi (道義), often simplified down to just ‘gi’ in English. It is very important that you wear your do-gi correctly when training, and take care of it outside of training. One important rile about wearing your do-gi is that the left side must always cross over the right side - the opposite is reserved for corpses dressed for burial.
When you remove your do-gi, both during training (e.g. for Sanchin kata) or afterwards, it is important that your fold it nicely. Here is a brief explanation for how to fold your do-gi:
Here is a brief video from Jesse Enkamp showing two different ways to fold your do-gi:
Your belt is known as your obi (帯). It is very important that you learn to tie your obi correctly. It should be even on both sides once tied, and worn above your hip bones (i.e., not too low around your waist).
There are a few ways in which to tie one’s obi. Here is a brief diagram explaining one of those ways which easily avoids having the belt cross over at the back:
And here is a brief video showing the same movement as in the diagram above.