Portal 2 (and of course the original Portal 1) is a great game, no doubt about it! But what do you do when you're stuck, and how do you quickly solve a test chamber? How do you survive on those hard challenge maps? How do you beat custom Portal 2 maps (and Portal 1 maps)?
Think outside the box!
Or inside. What do you have inside your cube? You need to figure out what you have at your disposal. You also need to locate the exit, or what you think is the exit. A clear goal will boost the time it takes to solve the puzzle presented in the test chamber, and it will give you the opportunity to plan carefully.
If you are stuck, or want a no-brainer solution - read this: take it one step at a time! If you don't know where to go or what to do, just do what seems obvious. You see a cube - go get it. When you get up there you might see what it's for.
There are a few examples of this in Portal 1, but many more in Portal 2. You need to preserve what you've already got. If you have a lens, try hitting two targets with it instead of one. Try to use the same portal multiple times. This is where I failed during my play of Portal 2!
Go with the flow
If you have no clue, just follow the map layout. Test chambers in Portal will often present a challenge, but it will also give you some kind of path to follow. Go get the obvious objects or press the buttons - the path will UNRAVEL what you should to. Sometimes this is required, sometimes this is a no-brainer solution. As mentioned above.
Look for details
It's all in the details, baby! Platforms turned 45 degrees indicates a jump, and platforms down below indicates a need for speed. This is unfortunate since it actually gives away the solution in many cases, but will help you solve a Portal test chamber. I don't recall a single detail or object that was not used, or could not be used.
Stop thinking with portals
This is ironic since you need to think with them anyway. Point is - try to use other elements, don't have the mindset of "portals are my main solution". Portal excursion funnels, gel and light bridges will help you a lot. Don't neglect these important inventions. If all you have is a hammer, everything will look like a nail. You will go mad when you find not portal-friendly surfaces :P.
As a final note (*I'm making a note here*...) YouTube has a ton of videos on Portal 1, and I reckon they'll have a ton on Portal 2 soon as well. Not that you'll need them to complete the standard game, though.