For repairing cracks in tile, homemade caulk won't do as good a job as commercially made caulk. And because caulk is so inexpensive, buying it will usually be your best solution in the long run. However, if a situation comes up where you need caulk immediately for a temporary fix, then you can make some caulk with a little baking soda and basic white glue.
The exact amount of baking soda and glue you'll need will depend on how much caulk you'll need. Assume 2 tbsp. of baking soda will make enough. Mix the baking soda with enough white glue (a craft glue works best) to create a thick mixture. Mix this in a bowl, on a plate or even on a piece of foil. Stir with a spoon or paint stirrer until the baking soda is completely dissolved and mixed into the glue.
For applying the caulk, as you won't be able to use a gun, you'll have to use the stirrer or other stick to work the caulk into the crack. Use more caulk than the crack holds, so the crack overflows. Then use a piece of cardboard to smooth over the caulk, creating a flush line. Let the area dry thoroughly before applying any paint over the caulk. For removing the temporary caulk to replace it with commercial caulk, clean the area with a sponge and water and use a knife or screwdriver to scrape it off.