How do I wire tanning bed in house and are the green and red ground

First, by the way you posed your question, I question your ability to do the work. I do not intend to slight you its just that your question lacks any knowledge. The safest bet is to get a licensed electrician to plan and install the project for you. Please consider that.

In a three or four wire circuit, Black & Red are considered to be Hot conductors. White or gray is Neutral. Bare, Green, Green/yellow are Equipment Grounding conductors.

Because you are adding to your panel, you are required to pull an electrical permit yourself or have you electrical contractor pull the permit.

If you choose to pull the permit, then you are responsible to repair anything that the electrical inspector finds wrong on the inspection of the work. You really want to pass the inspection to avoid any insurance problems down the road.

Now to the work, you must draw up a wiring plan and submit it to the LHJ when you pull the permit.

Things you need to know:

Is the tanning bed going to require both 240 and 120 VAC?

What is the total amperage required by the equipment.

From that you will know whether to
1) use a 2 conductor cable or a 3 conductor cable (both with ground). And what AWG conductor you need.

2) Required load (amperage)

3) Correct size of the breakers (you derive 240 VAC by using a dual 120 VAC listed breaker). This will take up 2 tandem breaker positions in the panel.

4) The necessary sizes of junction boxes based on cable fill requirements of the NEC section 316.15 or 16.

5) You are also responsible for pulling the cable from the panel box to the location of the bed's outlet and the code requirements of the NEC code for installing the cable.

Do not do any work on the panel while the panel is live. You could get very dead, very fast.