The sub-cut and onward.

Strip piecing is such a common practice in quilting that there is hardly ever a pattern where you don't sew some pieces together and then sub-cut them into smaller pieces and re-sew them. Obviously there are patterns out there that don't have strip piecing, but most easy patterns have strip piecing.
So for my project, there were two strip-pieced units per block, so I'll go through the subcutting and sewing to complete one block.
Most strip piecing allows for a little to square up after stripping. You can see that my top strip set is off on the left hand side.
So I square up that strip set. Then I measure and cut (below).

I continue to cut the appropriate number of subcut units from each strip. In my case, I needed four subunits from each unit, plus the squares I cut earlier to make a block.
My subunits ready to go.
So I lay them out as they'll be in a block. Now to be honest, I would cut ALL of my subunits for ALL of my blocks and then chain piece them, BUT if you are at all worried that you'll get things switched around, do it one block at a time. There's nothing wrong with doing that, because if you get them mixed up, it won't be faster because you'll have to rip.
I'm a chain maniac, I chain not only everything in one quilt, but I'll chain multiple projects at a time (and yes, that has led to some interesting sewing mishaps--the price you pay to be a quilting speed demon).
There's my block laid out and ready to be sew. I'll sew it in rows with three subunits per row.

Before you sew, lay the pieces together and see if there are any seams that should match up. If there are, you'll see the reason that the direction you press your seam matters. When seam lines match up, you can do something called locking the seam by butting the two ledges of the seams against each other. From the side it would look like this:
See how they're pointing opposite directions? That means when you iron the seam you're about to make, it will lay nice and flat and you'll get a nice precise point that way.

If something should go wrong as you sew the seams, you will have to rip. Many sewing machines come with a seam ripper, but they're usually dull and small, so I recommend getting one at your local quilt shop. You will need it at some point.

There are myriad ways to rip or unsew, but the one least likely to stretch your fabric is to slide your seam ripper under about every third or fourth stitch and cut it.

See how the ripper blade is under the stitch, but not cutting the fabric. Do that all along the seam, every few stitches.
Here's a seam ready to finish the rip (if you can see it :) Now gently pull the two pieces a part and one side should have a bunch of little threads and the other will have one long piece of thread. Pick these out and you're ready to resew.
Here I've got the three rows together. You always want to sew anything you can in rows (or columns) first. Occasionally beginning quilters get a wild hair and want to sew the four units in the corner together and then sew the others on. You will end up asking yourself how the hell to continue sewing it together. Most patterns are pretty good about specifying which things to sew together in which order, but some assume you can figure it out.

So finally I sew my three rows together, and I've pressed so all my seams will interlock. Here's the finished block:
And from the back you can see how neat the seam allowances look when all the pressing is done correctly.
Voila! One block down. Next time I'll show you how to put them together, then borders, then quilting, then binding!
Happy quilting!