In her book Green Housekeeping [1], Ellen Sandbeck notes that one simple way to avoid using chemical products when you clean is to use steam vapor instead, which loosens dirt, grease and grime quite easily, so they can then just be wiped off with a clean cloth.

Here are some of her tips for the technique, according to the Housekeeping Channel [2]:

• "To steam clean a wood, vinyl or tile kitchen floor, attach a clean terrycloth towel to the floor brush, then put the floor brush on the end of the steamer's extension tube. Use a mopping motion to steam the floor clean, moving quickly to prevent heat damage. When the towel gets dirty, turn it over or replace it with a clean towel."
• "Clean tile grout by using the steamer's detail brush, then use a towel-covered floor brush to remove excess moisture and residue. If the tile is very dirty, use the floor brush without a towel, then wipe the steamed area with a clean towel. You can use this technique for tiled counters as well as tiled floors."
• "Strip off old paste wax by using the floor brush to steam a small section at a time. Wipe off the dissolved wax before moving to the next section. When the job is done, clean the brushes with hot water before the wax has a chance to harden. Wipe down the surface with a clean dry towel before applying new wax."

Source [3]