You can have up to 6 active skills selected but you only get the abillity to add a new active skill at set intervals. In the beginning you can only allocate 2 active skills.
You also have 3 passive skills that unlock at set intervals. None of which are available at level one.
There are also no longer skill points to assign, if you are the level requirement for the skill you can use it as long as it is set to an active slot. It takes time to have a skill set to an active slot be available for use after it is first set. So you can't change mid battle and expect it to be ready in a moments notice. The other major change is that there are runes now, not available in beta, that drastically change what a skill does. This is where the customization of skills come into play, go look on the diablo 3 wiki for the info from E3 about what the current plan is for that.
Anywhere, anytime. The skill that you equip will be given a 30 second cooldown. During this time you can't use it or change it for another skill. Any skill on a natural cooldown also cannot be changed.