Holi typically takes place in the months of March-April (the exact dates vary from year-to-year since it's based on the Hindu lunar calendar). And indeed, it is a massive festival...in the Northern regions of India, since that's where the tradition is based. It is also celebrated in other parts of India in slightly different forms, but not the same extent.
Holi doesn't just involve playing with powdered colours, but also water fights with water pistols and water balloons. Suffice to say that if you're out on the streets during the festival, you will get soaked and caked in colours. The festivities drag on over multiple days. Another tradition during Holi, which you may come across when travelling around this time, is the consumption of bhang - an extract from cannabis that is typically crushed, mixed with water, and drunk to get intoxicated. (Recreational drugs are illegal in India but on this occasion it's pretty much overlooked because of "tradition").
(As an aside, the Thai festival of Songkran takes its roots from the Indian tradition of Holi, and is celebrated in somewhat similar ways with water fights.)
The powdered colours themselves can be bought from shops, or people will be more than willing to share with you as long as you agree to join them in celebrating. Concerns have been raised over the past few years on the safety of the dyes used in some of these colours as the cheaper ones tend to be made using metallic oxides. Dark blue and black colours tend to be of this kind. If you want safer dyes, ask for gulal (pronounced "goo-la-ahl") which are made from natural plant extracts and usually won't cause allergic reactions. Limited contact to the cheaper metallic dyes shouldn't cause problems for most people either; it's only long term exposure that can cause damage to skin, but it's something worth being aware about.
Indian expatriates around the world celebrate Holi too, so in case you're unable to travel, it's possible to get a taste of the festival at one of these celebrations. Check out this video at Festival of Colour USA - they can be pretty large scale events too!