I bought 2 anti-static gloves and 1 grounded wrist strap to protect the parts against ESD by assembling computers. I was wondering whether a single wrist strap is enough, because I use to touch parts with my right hand too.
Grounding yourself is only part of mitigating ESD. You can still cause damaging discharges while properly grounded when the device you're working on is itself charged, when the tools you use (like a multimeter or screwdriver) are carrying a charge or when your workbench/parts bin is charged.
Ideally you'd ground everything that can come into contact with sensitive devices:
Any surfaces where you may lay down your board and/or components
Any tools and equipment that may contact the device (soldering irons, electronic test equipment, screwdrivers, etc.)
This grounding can be accomplished either through your body (as is done with a dissipative screwdriver, side cutters and the like) or a dedicated grounding wire (e.g. an antistatic mat on your bench). Grounding leads must contain a high value resistor, so that you won't get shocked via your strap when accidentally coming to contact with high voltages. Grounded surfaces should be resistive (e.g. ESD mat, dissipative tray), instead of highly conductive (e.g. steel box, aluminum plate), so that any discharges that do occur will get current limited.
Do you really have to go through all this trouble? It depends. I personally don't bother taking all these precautions with hobby electronics or while taking my PC to bits (at my own risk). However, I do take this seriously at the workplace and I think you should do the same.
As the question written, "is one wrist strap enough", the answer needs some qualifications.
If you are concerned about touching parts with your other hand, then the body conductivity will provide discharge path for the entire body even with one wrist strap. So the answer is "YES".
However, this answer assumes that the rest of assembly environment is designed in full accord with ESD protection methods. Ideally, you need a ESD mat, and an assembly table with ESD-qualified surface, all properly grounded with leads having 500k+500k "safety" resistors. Check with some articles on ESD protection how to accomplish this.
There is really no answer to this question as written. Since ESD protection is really a probability thing, "enough" is meaningless.
There are also many variables that affect how much ESD you may be carrying. What you are wearing, what kind of shoe or sock you are wearing, carpet or tile, dry air or humid, dry skin or moist, hairy wrist or bald, how much you are moving around... it all affects the formula
Enough also depends on what you are working on. Some devices are relatively insensitive to ESD. Others are so sensitive you need to work under ionized air.
In general, if your wrist strap is making good skin contact, you are pretty safe to work on general electronics. However, it doesn't hurt to get into the habit of touching something grounded with the other hand before you unpack a device or touch a circuit board.
One grounding point on your body is sufficient to drain any charge on your skin. We are not insulators, our skin is conductive and any static electric charge on your body will equalize over your entire body within microseconds.
You can dispense with a ground strap entirely by using ESD conductive shoes and working on a conductive floor or ESD mat that is grounded, and using a grounded ESD mat on your work bench. It is also advisable to wear an ESD smock over your clothing, as your clothing is actually one of the the primary sources of static charge.