Meaning if it is easy and accessible to try and fix your own things, or DIYing a solution before going to (if at all) professional assistance. Typically because the professionals are very expensive or a hassle.

Comes from trying to fix technology and other of the sort with small things that everyone has, such as toothpicks, because getting it professionally fixed is very expensive, and you might as well try.
John: man, my car is really acting up, but I can’t afford to take it in to the shop right now.
Emily: dude, just take a toothpick to it.

Sara: my phone speakers were absolutely trash earlier, but I took a toothpick to them and now they sound fine!

Eric: dammit, I need stitches but the American healthcare system is hell
Aaron: well, you know the drill. Pull up YouTube, we’re just going to have to take a toothpick to it
Get the Take a toothpick to it mug.