Northern Chinese dialects commonly have 3,4 or more tones. Southern dialects are typically more conservative, preserving more tonal distinctions, such as Cantonese (Yue4),which has 8 tones. Very rarely, even more complex tonal systems are encountered.

Happily enough, Mandarin is decidedly on the less-complex end of the tonal spectrum; these tones are fairly easily described and learned.
Mastery in speaking them is another question!

Borrowing a system devised by the emminent linguist Zhao4 Yuan2 Ren2 to describe tones, we can use a numerical scale to describe the relative pitch of the tones. Using a scale numbered 1-5, with 1 being your lowest, comfortable speaking voice, and 5 being your highest comfortable speaking voice, we can describe the four tones in Mandarin as follows:

Remember that the above values give you a description of the pitch contours of each tone; the four tones found in Mandarin are not relative to each other. With the exception of the first tone, each tone starts and ends in a different register.

A handy, if inelegant, way to denote tones is to simply add the numbers 1-4 at the end of each syllable. Thus, "I would like a bottle of beer" becomes:

"Qing3 gei3 wo3 yi1 ping2 pi2jiu3"

An important note: Mandarin is famous for its' "Half-Third Tone", which simply means that when followed by any tone other than another third tone, it stays low. The half-third can be described thusly:

Just to make life interesting, whenever followed by another third tone, the third tone becomes a second tone.
So in the example above, the "Qing3" and "gei3" are actually pronounced as second tones; only the "wo3" is spoken with the full third tone's dip-and-rise contour. Be careful with your third tones!

Finally, it should be noted that Mandarin has an "unstressed tone", which as the name suggests is simply an unstressed syllable. Technically speaking, this is also a tone.