Navigating the London Undergroun

First off, start here: http://www.tfl.gov.uk/assets/downloads/standard-tube-map.pdf That is a map of the entire system. Transfers between lines are clearly marked and is usually all underground. Just follow the signs.
However... Who gave you these directions? The Backerloo line does not go to Canary Wharf. If you are trying to get to the tube stop called "Canary Wharf" from the airport, you need to transfer at Green Park to the Jubilee line towards Stratford. :)

Almost always the two lines will be at different levels. This means stairs or (sometimes) an escalator. Signs on the Underground walls will indicate how to get to the line you want. They will often say "east" or "west" etc. Check your map. There are also large Underground maps posted inside the stations. I always carry a pocket-size Underground (Tube) map with me.

Hi Nicholas, It was the 'journey planner' at tfl.gov.uk web site. It said to take the Heathrow Express towards London Paddington Rail Station, walk to Paddington and take the Bakerloo line towards Elephant and Castle Underground Station to Baker Street Underground Station, then change at Baker Street to Jubilee Line towards Stratford Underground Station or Jubilee Line towards North Greenwich Underground Station to Canary Wharf Underground Station.

If you will be taking the Heathrow Express, you can go down and take the Bakerloo line to Baker Street. Transfer to the Jubilee line going to Stratford and go all the way to the Canary Wharf underground station. If you are taking the metro from Heathrow, take the Picadilly to Green Park and transfer to the Jubilee line going to Stratford there. Again, go to the Canary Wharf stop. You will find the signage to be amazingly good. As you go down into the metro, you will clearly see signs directing you to the correct train. As you get off a metro, you will see Way Out signs and signs with train names on them. Follow the signs through the myriad of passageways. As you get closer to your new tracks, the pathway generally divides depending on which way you are going. At the divide, you will see complete route maps painted on signboards that clearly show all of the stops from where you are at to the end of the line. For the Jubilee line you want, it will be Stratford. You won't get lost. Here's a couple of hints for the London Underground based on our experience. 1) Most of the people you encounter changing trains in the underground passageways are going in the opposite direction you are. 2) There are reportedly over 400 escalators in the London Metro system. Try and find one. (I'm teasing. You'll find one every now and then but there are a lot of stairs).

Linzi, As the others have said, the signage is good and you can get a map of the system, so it's hard to get lost. I can walk the wrong way down a block on the street, but I've never gotten on the wrong underground train. Even if you do get on the wrong train, the cars have maps in them, and the stations are announced, so you can quickly tell if you're headed the right way. Just a tip on the journey planner on the TFL site: if you click on "more options" you can eliminate types of transportation (like if you don't want to take a bus as part of your journey, or you want to skip trains like the Heathrow Express) and you can even tell it you can use escalators but not stairs if you want to try to avoid hauling luggage up and down staircases.
Enjoy your trip!

Thank you to everyone for all your wonderful advice. :) I'm not as worried now so thank you ..lol. I don't know why but I had visions of the Underground being some dark tunnels, poorly lit and like an old movie..lol.
Am looking forward to my trip and feel now I won't get lost..lol

You won't save any time by taking the Heathrow Express and you'll pay a lot more. As Nicholas said, take the Piccadilly Line from Heathrow to Green Park and the Jubilee Line from there to Canary Wharf.

Everyone has given you excellent advice. When changing lines, do be prepared to walk (sometimes a lot), and to change levels (sometimes with escalators, but often with stairs). You never exit a station to make a change (if you do, you get charged a new fare). Just follow the signs to the next line you want, and follow the crowds (many people will be making the same changes you will). Things to be prepared for: 1. Gazillions of people will be using the system, all in a hurry to get where they're going. Don't be intimidated. 2. Almost everyone will know where they're going, so they can have the glazed or bored look of someone who's "seen it all." Again, don't let this bother you.
3. Numbers 1 and 2 mean that help is always around, and that most people in the underground can help you if you just ask. Don't be afraid to ask for help if you start to feel lost or paralyzed. There are maps in multiple places in the tube, but it still helps to carry one around (if your guidebook doesn't have one, get one that does). There can be more than one way to get somewhere (as you're already learning), and many of the stations have service on more than one line (as you can see on the map). As long as you know this, it's not a problem. After a few days, you'll get the hang of it like a pro.

Ah. I see. I was thinking that you would take the tube all the way in, which can be done from Heathrow on the picadilly line , although it takes longer.
If you take the express, then yes, Bakerloo to Jubilee. Everything should be easy to follow and understand. :)

The Underground interchanges are very well marked. You undoubtedly will change levels, but dont go out the exit gate at (grounfd level0 else you will be charged for another journey when you re-enter. If you are travelling in rush hour you will find the other commuters racing along corridors and up and down steps. Dont let that intimidate you. Lag behind and take your time so that you are comfortable you are going in the correct direction And definitely carry a pocket underground map with you

Every Underground station will have little 3-fold Underground maps made of light card. Free, from the literature display near the ticket machines and the ticket windows. Baker Street Underground station, one of the very first underground railway stations in the world, is really neat - with vignettes of Sherlock Holmes stories on the tiles around the station and along the platforms. BUT, with so many lines converging in one place: Metropolitan Circle Hammersmith and City Jubilee
Bakerloo it can be a bit confusing to the first time user, especially if you are humping luggage around. It is lovely, with lots of dark wood and plenty of tiles, but it has multiple passageways to different parts of the station and multiple routes to connect between lines. If you just have a backpack and want to have a look around, and don't mind being a touch turned around go and explore it. I love it, for architecture I think it is the best Underground station in England. You may decide that one change at Green Park is all that you really want to do and take the Piccadilly from Heathrow. Much of the outer London bits are above ground, but it is quite a lot of stops. I don't think there's much in it between the routes, time-wise, and because I'm cheap I'd probably keep my money to myself rather than using the Heathrow Express and making 2 changes.

Wow, talk about great replies.. :) Thanks to you all, and you know who you are..lol I won't be in any rush, so I like the idea of being able to take some time to take in my surroundings. It was also just the original thought of lugging my suitcase and laptop bag around with me, and having so many people rushing past trying to get where they are going (probably work at that time in the morning..lol - I arrive at 6.30am on a Thursday morning). Of course that is the time the plane lands, by the time I get through customs and collect my suitcase it could be 7.30am :) I probably won't be taking the Heathrow Express after all, because even though it's by far the quickest of the trip options I can't justify spending the cost of that ticket...lol. I've already purchased my Oyster Card so that will cover me for the underground trip to Piccadilly and on the Canary Wharf. Plus I like the idea of just one change. Once I've recovered from jet lag and don't have the suitcases to cart around, then I can take my time and travel around and not have to worry about getting in someone's way...lol. Once again, thank you to everyone who has helped..you guys are awesome. :) Wish I could pack each one of you in my suitcase and take you with me..lol