The tape tip helped me quite a bit. Until I got it, though, I did things a little differently. I cut my border fabric just a bit larger (about 1/4 inch) than needed. After sewing the border on, I squared up the block using my rotary cutter and mat.
Let's say you need a finished 2 inch border. You'd cut it 2 1/2 inches. I cut it 2 3/4 inch before sewing. Make the seam and press.
Measure carefully from the seam to the edge of the border and cut so that you have a straight edge. Using the 2 inch example, you will cut so that the block will be 2 1/4 inch. (Remember you need that 1/4 for the next seam.) Anything over 2 1/4 gets cut off. Turn the block and place the new edge on a mat line close to your body (it's easier to see so you can line everything up). Again measure from the seam, making sure the ruler is straight with the mat and the seam. Anything over 2 1/4 inches gets trimmed. Turn the block again, measure, cut. One more time to get the final edge and you're done. Now the block should be perfectly square with neat straight edges, and your border is exactly what you need to continue on your way.