There is a pattern to the major scales, so all you really need to do is memorize the pattern, the series of whole and half steps comprising all major scales. The pattern is:whole step, whole step, half step, whole step, whole step, whole step, half step.
This is easy enough to see on the piano, where the whole and half steps are right before your eyes. Once you have memorized the pattern, you will know where the whole and half note steps are in any key. You just start with the note the key signature tells you to and adjust from there.
Once you get a sense of this on a keyboard, you can begin to practice each scale on the clarinet. To really get this, you have to get it in your fingertips, too, not just in your mind. When I learned to play the piano, I had to practice those scales hundreds of times. I wasn't too happy about it then, but I own them now!
A good way to learn scales is to memorize the circle of fifths. This can tell you what order the scales go in and how many flats or sharps are in a scale and wich ones they are. If you need a mnemonicdevice to help you memorize the order of sharps, a good one is Fat Cats Go Down Alleys Eating Birds (FCGDAEB).