yoinked my method frmo the official thread: dunno if it will be helpful.
no one seems to need help with it anymore, but seeing as its come up a lot I thought I'd give my methodology for the tile sliding puzzle. Maybe its just unfound pride in my own solution, but I always thought my way was the easiest.
for explanation think of the tiles as numbered 1-8 where the solution is:
123
456
78
step 1. get tile 1 to its solution position
step 2. get tile 2 to tile 3's solution position
step 3. get tile 3 below tile 2. puzzle should now look like this:
1x2
xx3
xxx
step 4. move tile 2 into solution position followed by tile 3 into solution position.
123
xxx
xxx
step 5. get tile 7 into tile 4's solution position.
step 6. get tile 4 into tile 5's solution position.
123
74x
xxx
step 7. move tile 7 into its solution position, followed by tile 4.
123
4xx
7xx
step 8. rotate the final 4 tiles until solved. I'm pretty sure in the case of a 3x3 puzzle, its impossible to reach this point such that rotating the final 4 won't yield the correct solution.
For those that are curious about larger puzzles, this is a recursive solution. You always apply the same ideal to the top most row followed by the leftmost column. Always solve all but the last two on their own, and then apply this 'trick' to get the last two pieces of the row/column into place.