Assuming that it is an old metal tub which has never been painted.
First - the tub should be thoroughly cleaned. To do this, wash it with soap and water, or with soda, or with sapolio, in order to get off the grease; then rinse out with clean, hot water wiping dry with dry cloths.
Then roughen up the surface of the tub by going over it with fairly coarse sandpaper, and wipe out the little dust and dirt produced by the sandpaper with a dry cloth.
The tub is now ready to be painted. The first coat should be white lead in oil thinned with turpentine, using a flat bristle brush in putting it on and being careful not to get on too thick a coat. Allow this coat to dry for at least twenty-four hours, when a second coat of this same lead should be applied in the same way and allowed to dry also for at least twenty-four hours.
The tub is now ready for the coat of enamel, using a kind especially made for such purposes. Open the can and stir the enamel thoroughly and apply with a flat bristle brush, carefully and evenly. One coat of this enamel is sufficient, which should now be allowed to dry from four to six days.
When you again commence using the tub do not allow hot water to run into it first, as it may soften up the enamel. If the tub has been painted in the past, the old paint should be scraped and sandpapered off before painting.