In order to be able to count strokes and more efficiently look up characters that you don't know, you need to be able to break them down. Seeing 購 for the first time is certainly intimidating, but when you can break it up into 貝 on the left and 冓 on the right it makes things a bit easier (although the right side is still tough). This gets easier the more you see them, because you will become familiar with the right side from characters like 構 and 講.
A big part of breaking up the characters is knowing the radicals. There are 214 of them traditionally. There's a list of them
WWWJDIC: Word Search page. That page lists the full forms for some of them, and not for others, though, so you have to be a bit careful. For example, 齊 is listed instead of it's abbreviated form 斉, but 艹 is listed instead of 艸.
After the radicals there are the phonetic components. 冓, from above, is an example. All of the characters I listed above, including the phonetic itself, are read こう. Some 85% of the characters are constructed by having a radical and phonetic. This can be helpful when coming across a new character. For instance, the other day I came across 楊枝, and while I had never encountered the first character before, I was easily able to remember its reading (although this particular phonetic isn't so neat as the one given above). Looking it up is no problem either, because I can see that it's made up of 木 and the phonetic 昜.
Of course, I'm assuming you can look up characters in your dictionary by components. If that's not the case then you'll just have to guess at readings, but I think most electronic dictionaries nowadays have that option.
Now, there's a book that teaches the writings and one key-word meaning only for each character, and it goes through 2042 of them by starting with small parts and building characters from them. Some people don't like this method, and others do, but the apathetic person seems to be rare. If you search the forum for "Remembering the Kanji" and "James Heisig" you can find discussions on its merits and demerits. There's also "Kanji and Kana" that's a widely sold book, and others as well that deal with kanji and how they're used.
That's a little bit of advice, not knowing how much you know. I hope it helps somewhat.