I can't really give you tips on healing as a Shaman as I play a Disco Priest but I'll give you a few pointers that I have learned while levelling my priest from 1 to 80.
The first thing I would do (which I completely missed until I was about level 72) is to get yourself a healing add-on. I use "Healbot" but there are others out there...try a couple and see which one suits you the best. I was doing OK at healing but "Healbot" makes things a lot easier and thus making you so much better.
Secondly, learn what your healing abilities do, how long they take to cast etc. There is nothing worse than getting to the end of a long cast healing spell only to find that your intended target is a bloody, beaten mess on the floor. Know when to cast that small heal spell that will give you enough time to cast a bigger heal. Learn how much your spells heal of what length of time and use that information to be as efficient as possible.
Thirdly, develop a thick skin. Healing is a thankless task but as a healer you really are the glue that holds a party together. I have been blamed for party wipes on more than one occasion (a couple of times it really was my fault
). Unfortunately you don't often get compliments on your skill as a healer are few and far between and even a simple thanks doesn't happen that often. Having said that I had a great compliment last night in PUG - a tank asked if people wanted to do another random and the reply from on guys was "Not with you as a tank...the only reason we made it though that was because Kayal heals like a demon on speed". Which was nice.
Hear that Tanks and DPSers...say thanks to your healer...we like it
Mana potions...they really are useful. There were several points in my levelling of my Priest (Kayal) were I found that I didn't have enough base mana or fast enough regen of mana. A simple solution to this is to have a little stock pile of the best mana potions you can use. This helps for two reasons - firstly if you are in an instance and you run out of mana part way through a big fight it gives you an instant hit of mana that could be the difference between a wipe and success. They can also be used to reduce down time between fights in instances. Some people don't like hanging around for mana breaks every couple of minutes so it helps to keep the flow of the game going.
Having said all that about potions you should aim to have the best balance you can at all levels - pay attention to how much spirit and intelligence you have to maximise your potential as a healer. Oh and spell power is pretty key too
Oh and the last thing is...have fun. Really if you don't like it then don't do it. I enjoy healing people but many people hate it. In fact I prefer it to DPS or Tanking...but then I'm a be weird.
Hope that helps.