Probably one of the easy way is to drive. But I went that using National Express coach service, departing from Victoria Station in London. Megabus.com should be a good option as well as if you book the ticket earlier, you can get very cheap price.

How to go around there?

We (me and my friends) reached in the bus station and then take a walk to Blue Reef Aquarium. Later that evening, I took the bus and get around. I should say that it will be worth to buy a daily pass ticket (called as First Day Ticket; ask from the driver when you get into the bus) and go around.

Get a map before you go, either print it on the internet or take it from visitor information service and just see which bus goes to which place. Not that difficult as there is not many roads, so you can simply spot it. Look at the bus route and pick the right bus.

Use online map to locate the place you want to go

Once again, I love to suggest using maps.google.co.uk and simply type the place you plan to go and make a note of where the location is.

A sign in Portsmouth