You can arrive in Venice in a number of ways: by air, train, car, bus or cruise ship. The following section describes how to get from your point of arrival to the City centre. 
Getting to the Centre from the Airports 

The following paragraphs describe the various ways of getting from Venice's two main airports to the city centre, ie the main island. If you are staying in the Mestre (ie the mainland), your best option is to use the local bus or a taxi to get you to your accommodation. 

From Marco Polo 

You have four main options available, each of which comes with a variation in journey time and price. Much will depend on what you are prepared to pay and what time your flight arrives. Venice tends to close down quite early and so if your flight arrives at 9pm and you need to eat, you're probably best advised to take the fastest option. 
Water Taxi 
Quick, spectacular but very expensive! The water taxis are smart motor launches that will whisk you across the lagoon and drop you outside (or very close to) your hotel. They cost (as at March 2023) 120 Euros and take approximately 20-30 minutes to get you to your destination. NOTE: For some hotels you have to pay a surcharge of €15 to the driver because it is more and more difficult (and time consuming) to reach them because of congestion on the narrow canals.
To book a water taxi go online here (and receive a discount), exit Arrivals and look 45 degrees to your left. The water taxi desk is on an island in the main concourse. You pay the staff here and then exit through the main doors of the airport building. Follow the signs for water services and take the escalator to the upper floor to walk under a covered walkway to a newly refurbished waterside transport area. Note: the walk is around 500 metres. Here you hand in your ticket to the supervisor who directs you to the waiting taxi. Hint: watch for the signs to the TAXIS else you'll find yourself at the water bus service (see below). Note that the system for payment changes occasionally and so you may go to the desk to get a ticket but will actually pay your driver on arrival (in cash). Go online - it's easier.
A point to consider: If you've taken a cheap flight to Venice, you could end up paying more for a single taxi trip than the cost of your return flight. That said, I always take the taxi into the city just to avoid the inconvenience of Piazzale Roma (see below). And, of course, if you are a party of four or more, the price per heads becomes more reasonable. 
Water Bus 
This service is operated by Alilaguna. Follow the same route as described for the water taxi to the waterside transport area looking, this time, for signs to the water bus. Tickets can be purchased from the Alilaguna booth in the airport or at/on the boat itself. There are various lines to choose from depending on your final destination. I would attempt to explain them but by the time I'd done so they would have all changed. You can get information from the booth or there is, usually, a conductor/ticket seller waiting at the embarkation point. Tickets cost about 10 euros but may be slightly more or less depending upon the service you take. 
Hint: If you are in no rush to get to the city - the trip takes about 1 hour 15 minutes -, this is not a bad way to arrrive. The boats can be noisy and vibrate a bit but, particularly if you take the slower Blue line, you get a nice introduction to Venice from the lagoon. An hour before sunset is perfect as the wonderful light of Venice comes into its own. The service includes stops at Fondamente Nuove and the Lido 
Road Taxi 
There are usually plenty of taxis (ie the ones with wheels) outside of the main airport building. If staying in the Mestre, this is probably a good option as they can take you direct to your hotel. If staying in Venezia (the historic centre), you can take the taxi to Piazzale Roma. This is the main entrance point to the city reached across the causeway connecting the mainland to the city. This is at the northern end of the city complex and motor vehicles cannot go beyond this point. 
Once you arrive at Piazzale Roma, you need to complete your journey by vaporetto (water bus - see the Getting Around section). You'll need to buy a ticket from the embarkation point. The bus stops and ticket offices are situated close to the modern bridge that you can see from the bus station/taxi stop. They are easy to recognise by their distinctive yellow signage. Hint: this is where homework comes in. Venice can be a little confusing initially so make sure you have a clear idea of where your accommodation is located and the nearest vaporetto stop to it. Then buy your ticket and ASK which boat you should take and where it leaves from (all the stops are within fifty metres of the ticket office. This is because some vaporetti go straight down the Grand Canal - the main route through the city - whilst others turn off to the East. As a general guide, if you are staying in the centre of the city, the Number 1 (stops everywhere) or the Number 2 (express service stopping at main locations) taken in the direction of St Marco are likely to be the ones for you. 
There are services available from two transport organisations: ACTV and ATVO. ACTV is a public bus service and is the cheapest of the two with a fare to Piazzale Roma costing around 2 Euros. If you have a lot of luggage this can be a little inconvenient as you have to take your luggage on board. You may, therefore, want to check out the ATVO option as this has proper luggage compartments. Tickets can be bought for the from the transport office in the main arrivals hall of the airport. The bus stops in front of the airport building (just a short walk) and the service you need is the No 5. 
ATVO can be recognised as a blue bus with the ATVO logo on the side. Tickets (3.00 Euros) can be bought from the ATVO office in the arrivals hall although there is also a ticket machine near the bus stop (again just outside Arrivals). Bear in mind you'll need change for this and the machine itself can be a bit confusing to operate if you're not used to it. Tickets need to be stamped/validated in the machine inside the bus itself. 
The main advantages of the ATVO service are that it is non-stop and has luggage compartments in the sides of the coach making your journey more comfortable. 

From Treviso
As with road services from Marco Polo, your destination from Treviso airport will ultimately be the Piazzale Roma. To reach there you will need to take the ATVO bus service (the blue bus) from the airport. Tickets cost 5.00 Euros and can be obtained from the ATVO ticket office in the airport. Treviso is a lot further out from the city and the journey takes around one and a quarter hours with stops at the Mestre (where, of course, you may be staying). Note: On my last journey the service IN to Piazzale Roma was direct and took only 30 minutes but coming OUT was a slow crawl of 75 minutes through the Mestre. I cannot say whether these times are typical as I've only done the trip the one time. 
Treviso serves Ryanair and Transavia and ATVO arrange their timetable to match the arrival times of the airlines. I have to say that the bus service was very good (in terms of availability) and there is now an extra service provided by Barzi another bus company whose tickets can also be bought at the airport. 
Arriving by Road (Bus or Car)
Whether driving yourself or arriving by bus, your journey will end at Piazzale Roma - the bustling entrance to the historic city centre. With no roads in historic Venice (that's right, none at all although Mussolini once considered tarmacing over the Grand Canal in the name of Modernism....) you can go no further than this. Car drivers will need to park in the multi-storey car park and bus travellers embark and both will need to follow the instructions above to use the vaporetto for onward travel. 
By Cruise Ship 

Cruise ships arrive at the main port. This is situated at the North Western end of Venice's City centre. Your cruise company can probably advise on the best method of reaching the centre but, by default, this will mean getting to the Piazzale Roma or, if arranged, to an embarcation point for the vaporetto or a water taxi.

Note that in March 2023 the port was devoid of cruise ships and this may be as a result of the campaign to stop them from using using the Giudecca canal