EVE New Citizens Q&A

You can have multiple waypoints but only one destination. it's mostly used for convenience.
The autopilot follows waypoints in the order you entered them, by default it also pauses the autopilot when reaching a waypoint. Sometimes you can also use them to get the AP to use a specific route (e.g go from A to B, but travel through (waypoint) C).
Using the 'autopilot' part in the map menu also allows you to 'optimize' your autopilot for multiple waypoints, generating the shortest route possible to visit all of them.

So if I plan to visit several destinations, I'd set a waypoint for each and then either autopilot or warp to as usual, and it will take me to each one in turn? And if I simply autopilot it will stop me at a waypoint, where I can then dock and then once undocked simply activate autopilot again?

Since crucible you can even set the stations themselves as waypoints and it'll automatically dock you there, then when you undock you just turn on the autopilot to carry on your journey. So you just setup your route at the beginning and then don't have to worry about it again.

On another note, you might want to take advantage of the blocking functionality to force the autopilot to avoid certain systems like Rancer and Amamake (i.e. low sec ganking spots on the shortest routes between the trade hubs)

Using an autopilot can be dangerous. It warps you 15km from the gate and approach before jumping (usually you manually warp at 0m and jump right away). This approach can take a while and it's the time when you can be attacked. AFK flying is not a good idea. Also, because of this approach, entire journey takes longer the more jumps you have to make.
You can use waypoints to quickly plan your route when flying through unknown systems. For example, when you are at station X and have to pick something from station Y. Set your destination to Y and then waypoint to X. When you arrive at Y and pick your item(s) you already have a route back to X plotted. No need to look up system names etc. It's very useful when doing missions where mission goal is located more than one jump from the agent.
Remember: setting a destination clears existing route. When you have waypoints, stations on the way are not marked in yellow (don't know why), even if you set a waypoint on them.