It's called a "plunge cut". This particular method works with a sawzall, sabersaw, handheld jigsaw, or whatever you want to call it.
You've all learned the drill-holes-for-sawblade technique already in industrial Arts class.
For this plungecut method, you don't drill any holes.
You just start the saw, rest it on its guard, rock it forward, and BELIEVE!
If your faith is pure and you do it just fast enough the blade doesn't stub its toe and get bent.
In these pix Fungusamungus and myself are cutting slots for a skeg box on a CLC boats "Pax 20" kayak.
Step 1: Rest, Rock, Believe, Cut.
Rest the blade guard thing on the work. Usually the guard is just big enough that you can do this without the blade touching the work.
Run the saw and rock the oscillating blade down into the work.
If you're not confiden't you'll spend some time watching it waggle around gouging scratches in a fan-shaped pattern.
If your faith is pure it'll just gouge one scratch that gets deeper as you rock it down until it goes through the material.
Then raise the saw vertically and continue the cut in the normal manner.
Once you have the trick working you can do cuts through beams, doors, and other thick material.