platyhiker

There are two different strategies for leaders (and enders).
1) Use a scrap many times (usually until it is too full of thread to be used anymore), and then discarding it.
2) Deliberately plan to have fabric on hand cut and ready to piece to use as a leader/ender and then use this element in a quilt. (So this fabric is sown only once.)

So, if you're doing strategy 2, you might have a bunch of small squares on hand that you use when ever you are having a session of piecing. Let's say you sit down with your machine having nothing under the presser foot.
1) Get a clean start and piece two small squares together. To get the clean start, you can sew on a small scrap (to eventually be discarded) or hang onto your tails whiles you start on the squares.
2) As you finish the seam of the small squares, chain piece onto your "main" project. Keep chain piecing on the main project as much as you like.
3) As you finish your last seam on the main project piecing, grab another two small squares and chain piece onto them, sewing about half way down the seam. Cut the threads between the two small squares and the rest of chain piecing. Cut the threads between each of your chain piece elements, and set the two small squares used at the start aside for what ever project you will eventually put them in.
4) Go iron or do what ever you need to do ready for your next bit of piecing on your main project.
5) Come back to your machine and you already have your half sewn small squares under the presser foot to act as leader. Finish the seam on the squares and chain piece onto your main project.

So by planning ahead, you can always start and finish with the small squares, and avoid having to do (almost) any "cold" starts where you hang onto tails or use a scrap. As a bonus, you get a steadily growing pile of pieced items that you can use in another project.

If strategy 2 doesn't appeal, you can just adapt the above steps to work with two scraps and sewing half way down the second scrap as your ender, which gives you the similar thread savings of not having to do a "cold" start. When doing this, I like to have a handful of scraps near my machine, so that when I (temporarily) misplace one, I can just grab another one and not have to hunt for the missing one.