The reason to exfoliate is to remove the dead skin cell layer that inhibits the absorption of your moisturizer and your other skincare. This instantly makest he skin look brighter, cleaner, smoother and younger which is why it gets very addictive so be careful not to overdo it.
How often you exfoliate should be based on your skin sensitivity and the strength of your product. With most products and truly sensitive skin should exfoliate only once a week, most are fine with 2-3 times a week which is why this is what product packaging usually instructs (majority rules) and some tougher skins can handle daily exfoliation.

There are two types of exfoliation: Physical and chemical.
With physical, your scrub or cleanser will contain small grains which you literally buff into the skin to help loosen the dead skin cells. To some degree the type of grain (spherical and round is gentler, jagged edges like those of most natural sources are harsher) and the amount of particle used in the product (if it's more concentrated with the solid particles it will be stronger) have an influence on how strongly the product exfoliates, but the largest factor is how strongly you scrub. It is advisable to go gentle because it's hard to tell, unless you're very experienced, how much exfoliation is enough.
With chemical exfoliants, the exfoliant does the job for you. It works on a microscopic level (you don't see anything being exfoliated) to unglue the dead skin cells from the live ones and help them shed. The most common types are glycolic, lactic acids and salicylic acid. Glycolic and lactic are AHA's (alpha hydroxy acids) and they work largely on the surface of the skin and have some humectant effect, which means they draw water to the skin and plump it out. Salicylic acid is a little bit different, it exfoliates on the surface and inside the pore and has a mild anti-inflammatory effect (which makes it great for clogged pores and acne). It comes in almost every kind of product, most commonly in creams, serums, gels and liquids. To a lesser degree they're also incorporated into masks and cleansers (if you have particularly sensitive skin, these are preferable to use because they are rinsed off quickly and the acid doesn't stay on the skin). The concentration is important, for sensitive skin 1% is ideal for salicylic and 4-7% is ideal for glycolic or lactic. Skin that is tougher can handle more, 2% for salicylic and up to 10% for glycolic and lactic. Also consider PH, if the product's ph is between 3 and 5 on the acid-base scale, it exfoliates much more effectively.
Personally, I prefer AHA's and BHA's because they exfoliate more evenly and require less work from me. They have also been shown in some studies to have a positive effect on collagen production with continued use. I have strong skin so I use them nightly, under my moisturizer.

thanks guys! very helpful and informative