When I lived in the UK I used to do all the weekly maintenance on the tables in our local club. Firstly comments here are correct the nap of the cloth should lay down flat when running your hand from the brown spot to the black spot.
When cleaning the table make sure you have a good brush, horse hair if possible, a spray bottle containing water, a decent cloth, some polish and an iron if you have one. If you have an extractor fan use it while cleaning the table. Begin by brushing the table starting in the center of the cushion at the brown spot end and brushing towards the black spot, working outwards to the side, always brush towards the black spot, do both sides of the table. When brushing the inside of the cushions make sure all dust etc is pushed down into a pocket. When brushing the top of the cushion and rails do so with a slight outward motion so no dust gets back onto the cloth. Next clean out the pockets with a damp cloth ensuring you get all dust and debris cleared out, or the balls will pick this up.
Use the spray bottle and put a very fine mist of water onto the table a very fine mist. Make sure your iron is hot and ready to go, most have a light on to signal temperature. Never, never iron the cloth without running a clean rag over the base of the iron first when its hot, an old spare piece of cloth is best for this. I found the best way to do this is as you brushed the table, from the center of the cushion at the brown spot end towards the black spot working your way out to the rail, then do the other side. Lastly clean your rails using polish, unless yours is a particularly old and well maintained table a can of spray polish works best. If you do not have an iron I would simply get another piece of surplus table cloth damp it slightly and brush it down with that after initial cleaning, it will help some.
I would do this weekly and polish the whole table about once a month, hope this helps.
