In order to create a functioning marker, you will first need an object in which to encase it. The easiest and least expensive option is a large glue stick that has had the glue removed. Other options include PVC piping or a large plastic marker that has already run out of ink.
To avoid drips and leaks from the bottom of your glue stick marker, you will need to seal it with a water resistant material. You can use sticky tack, hot glue, chewed-up bubble gum, caulk, or other similiar substances you may have around. Make sure to seal the bottom completely or all of your ink will seep out before you have a chance to use the marker.
Mix ink or paint with small amounts of paint thinner until you get the consistency you want for the kind of writing or drawing you'll be doing. The more paint thinner you add, the drippier and runnier your marker will be when you use it.
Once you've mixed up your ink and filled your marker, it's time to add a tip. There are plenty of materials you can use, including but not limited to: a chalkboard eraser, a large strip of denim, scraps of felt, cotton or corduroy, an old sock or a scrap of carpet. Take into consideration the surface you will be writing on when you choose the material for the marker's tip. If most of your writing will be on the concrete wall in your basement, use a tough material. For drawing on paper or fabrics, softer materials will give a better result. Once you've plugged the marker with the tip of your choice, leave it upside down for a few minutes. When the ink starts to drip through the tip, you're ready to write.