back ups and hard disks

I have been using my mac for a couple of years and love it but have never really got the hang of back ups and time machine. I have moved all my files onto a hard drive to save space as I'm running out but it hasnt helped as I haven't moved photos and music in case iTunes and iPhoto wont work if i do. I want to buy another hard drive for back up can you recommend one and advise how to do it. i have mostly music and photos and uni work on it.
also I havent really got the hang of how to use time machine.
i would like to understand also how to use icloud to save stuff so i can access it from other computers - mainly uni work so I dont always have to carry my computer.
I think a big part of my problem is that my iphone is my internet so i cant back that up either.
I bought and installed mackeeper but removed it after reading advice on the forum. I wish I had read that before I bought it. I thought it was ok cos it was advertised on this site.
Thanks

Sorry you bought MacKeeper. The site has no control over its advertisers I'm afraid. The mods have posted info on this elsewhere on the site.

Ok. Pretty much any external hard disk as big or bigger will do. Have a look around for prices suitable near you or at online shops you favour. Feel free to post on here when you find some if you'd like help narrowing the field.
As far as Time Machine goes its pretty straightforward.
Connect the external disk. Open System Preferences - Time Machine.
Turn time machine on and it will prompt you to select a disk, your new external. The time machine assistant will lead you through preparing the disk.
The first back takes some time. After that, when the disk is connected Time Machine will perform incremental backups without any effort from you.

Can you explain a little more about you iPhone/Internet/backup issue ?

iTunes will work if the music is on an external drive. You have to make sure the external drive with the music/media is connected when iTunes is launched. if not quit the program and relaunch after mounting the drive. iTunes for Mac: Moving your iTunes Media folder

This description of Time Machine is for an older version but the behavior is essentially the same. What is it that you are finding confusing?

Also look here.
Mac Basics: Time Machine