If you are prospecting by a creek with water, a shovel or small scoop. Classifier, pan, snuffer bottle or suction tweezer. Vial for your gold. A sluice is something you might want to get. That will get you started. As you get better you will want more equipment.
If you are in the desert you will need to dry pan. I have tried it with lead pellets and did very well. A metal detector or a dry washer.
Join a local chapter and they will have lots of members that can help you.
Good luck, let us know how you do.