Clean a floor drain with liquid drain cleaner or a manual or electric-powered auger, depending on how severe the clog is and where it is located. Not all drain cleaners are created equal; some are meant to dislodge fully clogged drains, whereas others are meant for work on the sides of the drain. Always read the instructions prior to use.
Get a socket wrench and remove the cover of the drain. It should twist off. After removing the drain cover, put on a pair of thick rubber gloves and remove any solid debris within reach, such as hair or lint; this can accumulate easily. Next, get an auger and thread it down the drain, twisting the handle clockwise to make the drill bit break apart any solid matter. Periodically pull the auger out to inspect and remove debris.
Pour a small amount of water on the drain to see if it drains as it should. If it does, the drain is clear. Otherwise, the drain-cleaning liquid is necessary. Follow the instructions on the bottle before use, such as ventilating the area thoroughly and wearing hand and eye protection. Don't use a plunger on the drain because backsplash could be harmful. After the drain is clean, replace the cover.