Hi epross1. Congratulations on your first trip (of many). Laurel and Anita have said just about all that needs to be said about your itinerary and length of the trip. I would add that you should take into account that you will use up 1/2 to a full day every time you change locations. Especially for longer than two week trips, you need to build a little "free time" into the schedule. You'll want to just kick back and relax occasionally, you'll need to do some shopping for things you run out of or forget to bring, then there's laundry and the unexpected.
Here are some details about your "how to travel around" question.
In Rome you get around by walking or taking the bus or the metro, depending on where you are and where you want to go. If you buy the Roma Pass (sometimes a good deal, sometimes not depending on how much time you have in Rome and what you want to see), you will have unlimited transportation for the 2 days of the pass. If you are there much longer and/or don't want the Pass, the TI used to sell a transportation-only pass good for several days. Rome is big, so you will probably want to use the bus and/or metro some of the time. Taxis are easy to get also.
In Florence get a hotel in the center. Everything, including the train station (Santa Maria Novella aka SMN is the one you want) is in walking distance. You may want to take the HOHO bus to get oriented, get to a couple of the more out-of-the-way spots. You can easily take day trips to Pisa (1/2 day) by train or Siena (full day) by bus. I believe there is a Florence card that includes many of the city's sites.
In Venice, you walk or take the vaporetto (water bus). There are also water taxis, but very expensive. You can buy passes for the vaporetto (various lengths of time) which are often worth it since the single fare is very high. It's nice to just ride the vaporetto - get a front seat if possible, if not then the very back for the best views.
In Paris you either buy a carnet of 10 tickets good for bus and metro, or you get a Navigo pass. The pass is weekly and runs from Monday through Sunday. Depending on the days you will be in Paris, it can be a good deal. Usually if you get 4 days out of it, you are close to breaking even, at 5 days you come out ahead. Paris is great to walk around, but sights are often far apart (and even for short distrances you may want to save your legs). The buses can be very slow because there is often a lot of traffic. The metro is fast, but you may have to walk farther to get to some of the sights - or to transfer trains. Again, depending on how much time you have and what you want to do, the Paris Museum Pass can be great. Even if you break even on entrance fees, it's good because you avoid some of the ticket lines. Also, you can just pop in to a sight for a brief visit, since it doesn't cost extra.
London to Paris. The best transportation is the Eurostar train. The best prices are if you buy 4-4.5 months in advance when they first go on sale. These are no-refund/no-exchange tickets so you are locked in. But the price can be as low as 1/4 or 1/3 of the full price. The Oyster Card is the way to get around London. There are several options and it can be confusing to figure out which is right for you. Using it is very easy, though. Everything I said about Paris applies to London - buses, underground aka tube, and walking.