There is a very nice Myth Busters video about bouncing a laser off the Moon linked below.
To answer your question, current work is done with an array of corner cube reflectors on the Moon roughly 50 x 50 cm in size. Pulsed lasers on Earth have traditionally been green frequency-doubled infrared Nd:YAG lasers, similar to the "classic" DPSS green laser pointers before they commercialized green diode lasers. That's why older green laser pointers were so expensive, heavy and large, they contained a semiconductor diode laser, and an infrared Nd:YAG crystal laser, and a frequency doubling crystal all on a tiny "optical bench" inside the pointer.
Don't be put off by the "peaks at 1 giga Watt" mentioned in the video, that's the instantaneous power during the very short, probably a few nanosecond pulse. The average power of the laser is going to be a few Watts or so. That's why each pulse contains "200 quadrillion photons".
The laser beam has to be collimated with a large telescope (like a meter or more in diameter) to make the spot on the moon small enough, and the received photons on Earth has to be collected with a large telescope as well. Each pulse usually results in only a few photons actually detected by a photomultiplier tube. You run for a while and collect enough photon statistics to average out the noise and get a precise time measurement. A special, very narrow pass optical filter is used to make sure light of other wavelengths on say the brightly lit lunar surface don't make it to the photomultiplier tube, or else it would just saturate.
You can read further about the retroreflectors in these Stack Exchange questions and answers as well: