Once you are in Venice there are really two main ways to get around: Walk or take a boat.
Everywhere within the main Venice island is walkable. It might take 20-30 minutes (even longer if you are going from the top of Venice (near the train station) to the south east corner), however it is always a nice walk. At night time it can be a little frustrating to be walking down a lot of back streets, trying to find where to go. However Venice really is a city that you can just get lost in and enjoy walking around.
You should definitely use your phone's GPS / Satellite Navigation. In some back streets there is not a good GPS signal, so you should have a rough route planned out in your head. If you get really lost, just walk until you find the big main canal, or the lagoon. You'll work it out eventually, and Italians are generally helpful and will try and help you if you ask them.
Major tourist attractions (e.g. the train station (Ferrovia), Bus station (Piazzale Roma), Piazza San Marco, Rialto) are often sign-posted with arrows. Often these will look like graffiti (the words can be spray painted on a building). You should trust these directions!
You have several boat options, all variying in different prices and durations.
The classic Venice way to travel! They are used exclusively by tourists. You can sometimes negociate (maybe €10 less). But remember that you pay per boat, so if there is a big group then it is cheaper per person.
You can find them everywhere in the backstreets of Venice, plus quite a few piers on the main Grand Canal.
This is a cheaper version of the Gondola rides. If you want to save money, or don't really care about spending 30+ minutes on a boat ride then this is for you. However, by the time you have taken a couple of photos and selfies you will already be at the end your journey. The ride takes about 1 or 2 minutes.
They are used by residents to get from one side of the river to the other. There are 7 Traghetto piers along the Grand Canal, and they are quite easy to spot.
Tourists tend to sit (if it isn't crowded - at night time it is generally less busy), and residents and locals will stand. If it is busy then you might have problems if you sit and/or have suitcases or bags.
There is a good guide on using Traghettos here.
They are worth doing, as they are really cheap. Just wait until you need to get to the other side of the river, then you have a good excuse to spend a couple of euros.
Pay the man (we haven't seen any women Traghetto workers!) when you get on. We have found from experience that they have change, but prefer it if you give them the exact change.
The boats will go backwards. So get on, walk to the other end of the boat, and sit facing the man who you paid. Then you will be facing forwards.
This is the normal water bus. For one trip they are really expensive! But, they are good for 2 reasons:
Not every pier has a ticket machine, but all the main ones do. Some have ticket boothes, where you can speak to someone.
Remember to validate your ticket (every time you get on the water boat).
These are another option, however they are rarely used by tourists. Just get walking! If you do insist on getting a water taxi, read here for details.