Is it possible and what supplies do I need to do so if possible

Asteroids are the same as any other planet/moon/comet. Yes it's possible, but not for all asteroids. Some asteroids are shielded, and you'd need the owner/controller to give you access.

The environment rules page should let you know what survival gear you would need on an unslabbed asteroid. However unless you find one in a hidden system at this point pretty much all the asteroids are slabbed so you do not need any special gear to walk around unharmed.

There is one more type of asteroids. Those are listed under ships, as wrecks. The sole purpose of these is to recycle them into raw materials. These you can not land on, dock in, or enter.