As someone who's got 1000 lines in Challenge mode, let's see if I can help you...
On the first level, the first thing to do, of course, is to get rid of the big '1' in one stroke. Once that's gone, all of the other sets of blocks that fall down can also be got rid of in one stroke, although I tend to draw a line, wait to see whether the set that's going to fall next can be connected to the first set, and if not, quickly tap the end of the line before the second set of blocks falls down. In level one, as long as you recognise the sets of blocks (there aren't that many variations), it's fairly easy to clear the level - just make sure you eliminate all the blocks in one set at once. Another advantage to being able to recognise block formations as they appear on the top screen is that you can draw the line on the grey bit at the bottom, then wait for the blocks to fall to the bottom (and 'underneath' the line you've drawn) so as soon as they hit the bottom you just have to tap to clear the set. This is particularly useful about halfway through each level, when a big letter is spelled out using two sets of four blocks. I think in the first level, the letter's an N.
Level two isn't that difficult - blocks fall down in sets of two lines. In most cases, just go one line at a time - usually each line will have two tiles that are the opposite colours to the other tiles on the line, so you just have to join them up, going over the dark grey area at the bottom. In some cases you can clear two lines at once if there are two of the odd blocks next to each other vertically or horizontally on the edge of the line. After around 50 lines, the sets of blocks that fall down are more like the ones from the first level - very easy to clear with one stroke. Just keep cleaing them in the sets they fall (don't try to connect the line to a set above it unless you can clear the whole of that set too), and before you know it, you'll be on around 185 lines. Now this is where you have to be careful. Don't clear any lines until you can see that the one that's about to fall down isn't the pink one. If it IS the pink line, make it so that it falls on top of ONE line at the bottom of the screen, and that that line can be cleared by one simple, short, horizontal stroke.
With two lines taken up at the bottom, start tackling level three. The first few sets of blocks that fall down will make a big '3', which will reach the top of the bottom screen, and can be cleared in one stroke (make sure you draw the line as the sets are falling down - don't leave it to the last second to start drawing it!). Then comes the it that I was stuck on for quite a while - the main part of level three. It can be very hard, and as not all the sets can be cleared in one stroke like you can do in level one, it's more difficult to give advice about clearing it. Just keep going on the practice mode, and try and get around 50 lines done. Once you've managed 40-50 lines in the main game, you can then (if you need to) get rid of the bottom line, which will make the pink one you've saved drop to the bottom and clear the whole screen. After that it's just a case of being quick on the draw, and recognising patterns. For example, there'll be quite a few situations in level three where you have to go along two or three tiles on the bottom line, then up to the next line and go across four or five tiles, and then go back down to the bottom line. But just keep trying on practice mode until you can do 40-50 lines almost every time!
Once you've done level three, levels four and five will seem really easy. Level four, for example, is a lot like level two, and you'll have to clear lines one line at a time for the first half. You may have trouble with level six, but if you get that far, you'll probably be good enough to work out how to do it yourself! Personally, I can almost always get up to level eight without much problem - it's then that you've got to be either really skillful or really lucky! But on the plus side, level ten isn't too bad! Just remember, on all levels except at the end of level three (you don't really need it in level 4) not to let the pink line touch the bottom until you're just about to die!
Good luck!