First off, the idea of the puzzle is to connect all the pieces by rotating them to form loops. The first 10 levels serve as a sort of training to help you get the idea of what you're doing. They're very easy to say the least. After that, however, the puzzles get larger and more complex. I'll go through the individual types of tiles and give you the best way to go about connecting them.
This tile is a beginning/ending piece. You can use it to terminate the ends of your loops. Remember too that 2 of these, pointed at each other, are considered a closed loop. Many times in a puzzle, you'll have 2 of these that won't need to be connected to anything else, so connect them together. These will never point to the outside of a puzzle, so if they're on the outer edge, start off by pointing them inward.
This is a standard curve tile, used mostly to fill in gaps and simply connect pieces of your loops. When these are on the outer corners of the puzzle, their ends will always point along the edges of the puzzle, like a rounded corner.
Here is your straight line tile. Again, pretty self explanatory, just be careful not to alienate parts of your loops with these. When one of these is on the edge of the puzzle, you can be certain that it won't point "out" as there's nothing out there to connect it to.
This is your "Y" piece. These may seem tricky, but they're usually not too bad. Often times you'll use 2 of these, pointed at each other, which will form an hourglass shape and help to close off your loops. With these, when they're on the outer edge of a puzzle, they will always point in, as there's nothing to connect them to on the outside.
Last but certainly not least, we have the "star" piece. These cannot be rotated but are one of the most useful pieces when starting a puzzle. Each point on the star must be connected, so its usually pretty easy to figure out (or at least narrow down) which way the pieces around the star should face.
Some parting tips:
- I like to star off a puzzle by going around the outer edge and making sure none of the pieces have points sticking out.
- The next step I usually take in a puzzle is to look for the "star" pieces and connect their points, this helps me start to get a good idea of where other pieces should go.
- When I work a puzzle, after i do the outer edge and the "stars", I like to start from one corner (usually the one with the most beginning/end pieces) and work my way out. This helps to get a feel of how the loops will form.
- When I only have a few unconnected pieces left, I usually try to "work" them towards each other so that i can make them connect together.
I hope these tips and tricks helped get you some badges, if anyone has more suggestions or things I may have missed, feel free to comment.