The bottom of your climbing shoe is usually just rubber. You can take a damp cloth and just scrub what ever is on it off, usually everything comes off. If not, you can try more aggressive things such has household cleaning products, or brushes to break down what ever is on the shoe.
Depends what you have on it. If you got paint on it, and it doesn't come off with water or by rubbing it off, then you could try putting alcohol or something similar on it, otherwise, you could use a soft wired brush to remove it.
The bottom of climbing shoes are usually just rubber, so keep that in mind when you use something to clean it, make sure it can be used on rubber and better to test it in a small place on the shoe that can't ruin it, just in case.
