Do you have a yarn shop near you that has a knitting group - or is there a local knitting group you could go to? You would find plenty of people willing to share patterns or point you in the right direction for your next project.
Blanket squares are a good idea - I have been teaching myself to crochet, and I am making lots of squares, in mad colours, and eventually I will make a random patchwork blanket out of them (random, because they are definitely not all the same size - I decided it was easier to decide up front that they wouldn't be the same size than to try to make them the same - I am not that good a crocheter).
There are lots of books out there - like the Harmony Book of Knitting stitches - that either have a few patterns in, or that are just books of different stitches - for striping, textures, lace, cabling etc. If you did squares of different stitches, it would rapidly increase your repetoire, and you could put the squares together into a patchwork blanket that would be uniquely yours.
Most stitches are based on knit, purl, knitting stitches together (or decreasing the other way, by slipping one stitch from the left to the right needle, knitting the next stitch on the left needle, then using the left needle to lift the slipped stitch over the last one you knitted, and off the needle - known as Sl1, K1, psso - pass slipped stitch over), and increasing by putting the yarn round the needle to make an extra stitch. Cabling is a lot easier than it looks too - you are basically knitting the stitches out of order, by slipping (say) 2 stitches onto a little cable needle and holding them in front or behind your work (as directed in the pattern), knitting the next two stitches off the main needle, then knitting the stitches from the cable needle. It sounds complicated, but it really isn't - and you can get some amazing effects really easily.