Hi tommy and

to the forum!
Unfortunately, even tho your friend's tank is mature, taking his water won 't help you much at all. The beneficial bacteria that convert the ammonia to nitrite, and then nitrite to nitrate live on things like filter media (sponges, ceramic balls etc) and also in gravel, plants and bogwood.
If your mate has not recently changed his filter sponges (in the last couple of weeks) they could really help you out by giving you a bit of their filter sponge. Make sure you don't take all of it otherwise he'll have some problems...!
It doesn't matter if your filters aren't the same, there is usually a way of fitting the sponge into the filter! Just make sure if you do get some sponge from them that they stay wet during transit to your tank, as letting the sponges dry out will kill the bacteria.
It is very highly reccomended that you get yourself a
liquid test kit such as the one honeythorn mentioned, API also do a master test kit, both around £20. This way you'll be able to keep an eye on what's going on in your tank. In the meantime you can take some tank water to your lfs (local fish shop) and they should test it for you. The downside to this is that ideally you need to test your water everyday so that could get quite tedious unless you have your own test kit.
While your tank is cycling, the ammonia and nitrIte and nitrAte readings will follow a pattern:
Firstly, your ammonia will increase to a peak, then will start to drop off (ammonia spike)
Before your ammonia reaches 0, your nitrItes will start to rise, then they will drop off (nitrIte spike)
Then your nitrAtes will start to rise (when your tank is cycled, you reduce these by weekly water changes)
Once your ammonia and nitrItes read 0 and you have a reading for nitrAtes, your tank is cycled.
Now, because you have fish in your tank already, it is very important to do 50% water changes a day,
ideally keeping the ammonia below 0.25 ppm (highlighting the importance of a testkit!) Ammonia, and nitrItes are very dangerous to fish, so they need to be kept to a minimum during the cycle.
If you keep up with the water changes, and testing, your fish should be ok! Don't hesitate to ask if you have any more troubles or haven't understood something, it can get quite overwhelming with all the information presented to you!
I hope this helps, keep us posted - once you get a test kit you can post your results up here to get help and reassurance.
Good luck
[edit: spelling]