We all know that when you arrive in a new city, especially one where you don't speak the language, you forget about the public transport and head straight to the taxi rank. I think this is a good idea when you are getting from the airport to your hotel, but using taxi's all of the time can get very costly.
So to start off, find out where the nearest Metro station is to your hotel/accomodation. Write the name of it down on something that you carry with you everywhere and walk to the station to familiarise the route to and from your accomodation. The reason I say to write the name of the Metro station down is that if you can't pronounce it correctly when buying tickets you can show it to the ticket sales (it is easier than getting frustrated trying to pronounce names like Barbes Rochechouart).
Ok, let's just say you are staying in Arrondissement 9 near the Moulin Rouge. Your Metro station would be Blanche on the Dark blue line no. 2. You will find signs near the Metro that have an M in a circle and a number in a coloured circle. So for line no. 2 you will see a dark blue circle with a 2 in the middle this means that on the map you will see the dark blue line with a 2 at either end this is a far as the no.2 train will take you.
For instance if you want to go from Blanche to the Arc di Triomphe you would take line 2 to Charles de Gaulle Etoile (very easy). Now after visiting the Arc di Triomphe you might want to go and see the Eiffel Tower. Charles de Gaulle Etoile station has 4 lines go through it, this may be a little daunting, but never fear look at your Metro map and find the line for the Eiffel Tower (it is on the yellow C line with a correspondence line from Bir-Hakeim station on Aqua line 6). From Charles de Gaulle Etoile find the Aqua line 6 (you are lucky it starts from this station) follow the signs to the platform, hop on and get off in 5 stops at Bir-Hakeim, when there look for the signs to Eiffel Tower(Tour Eiffel or Champs de Mars station) hop on the train or follow the crowds from Bir-Hakeim for a 5-10minute walk to the Eiffel Tower (just look for it and follow your nose, you can't miss it).
Now you won't always be lucky to get on the train from its first or last stop you will need to know which platform you need to be on to go east or west or north or south. Don't worry there are signs with all of the stations listed that the train stops at. So look for the line you want and check for the station then you will know which platform is the right one.
What if you want to visit Disneyland for the day? You need to find your way to Nation station where the above ground train takes you to Marne-la-Vallee station for Disneyland. You are in luck Nation in on line 2 (only 1 train from Blanche) and Nation is the end of the line. At Nation you will need to purchase the train ticket for Disneyland if you haven't already got it (ask for a return ticket). Now this is where I made a mistake and hopped on the wrong train, but if you find your way to the correct platform (the easy part) you need to then watch the lit up sign on the platform, it shows the station the train is going to when it lights up that is the train to hop on so watch for Marne-la-Vallee to light up and you are set. Get off at the last stop and follow the crowds to the Disneyland gates.
I hope I have helped you to have the courage to use the Metro in Paris, it makes sightseeing alot easier and you save on taxi rides.
If you would like to buy a Metro Pass to save time purchasing single tickets head to Paris Metro Pass.