I'll assume you've used the same size needles and same number of rows for each patterned square on each strip - so that the patterned squares are all the same length.
Use bobby pins to join the two strips to be seamed together. Make sure the start/stop of each square matches up the corresponding square on the other strip. Then you can either use a yarn needle with yarn to whip-stitch the two strips together, or you can crochet them together using either a slip-stitch or a single-crochet stitch.
Here's a neat variation - but it would take a bit longer to do: knit a narrow strip of like a neutral color - say black, or red, or white, whatever goes with your squares/strips - in a plain old garter stitch or rib stitch. Then you can simply sew a narrow strip to a patterned strip, using the same bobby-pin technique. And then match a second patterned strip up with the opposite patterned strip on the other side of your narrow strip. So you have your lovely patterned square-strips highlighted by the adjacent narrow strips.
Hope this helps,