The main type of reaction that alkenes undergo is addition.  This is not a trick, it is as simple as it sounds: an addition reaction is where two molecules react together completely to form one product (and only one product). e.g.:

Above is shown the reaction of ethene and hydrogen bromide.

The reaction above is an example of electrophilic (an electrophile is something that 'loves' negative charge) addition.  This kind of reaction is unavailable to alkanes, because we know that all their valence electrons are tightly held between nuclei, and are involved in bonding.  They are therefore relatively inaccessible.  However, alkenes can perform this type of reaction because they have a large amount of electron density above and below the line of the nuclei.  This leads us to the conclusion that this accessible cloud of electron density will act as a neucleophile (something that 'loves' positive charge).  In the example above, the pi bond acts as a nucleophile by attacking the proton bonded to bromine.

One important aspect of addition to C-C double bonds is Markovnikov's rule.  This rules tells us which way round an HX molecule will add to an alkene:  The hydrogen atom bonds to the carbon with the fewest alkyl substituents.

The reason for the preference of one side over the other (regioselectivity) can be seen if we look at the two possible intermediates of the reaction:

The one on the left hand side is the intermediate of the reaction above, the one on the right is the intermediate that would occur if the regioselectivity were the other way round.

What we must explain then, is why one of these intermediate is more likely than the other.  The answer lies in the fact that alkyl groups are electron donating with respect to hydrogen.  (This also manifests itself in properties of certain acids.)  What we note is that the most likely intermediate is the most stable one, and in this case, that will be determined by how well the positive charge is stabilised.  The most stable intermediate therefore, will be the one with most alkyl groups bonded to the carbon with the positive charge.

Iintermediates like the ones we have just seen occur quite frequently in organic chemistry.  They are called carbocations, and are discussed here.