What sort are you using would be my first question?
If you are using the "tongue/groove" sort, with the "cracks" between sheets, be aware that lots of "junk" can fall into those....
I would suggest you have a good vacuum and run it on hard floor setting at least every three days (more often is better) to minimize the gunk that can find a home there.
If you just sweep or "swift" you will get some compacted build-up.
For mopping, I use the O-Cedar
http://www.ocedar.com/?/p/microfiber-flip-mop-damp-dry-all-surface-mop
This fits on a specific mop head, but I love that it is great for a quick damp mop, as well as more intensive cleaning. And, they slip off the mop head and go in the washing machine.
I bought four of the pads five years ago and they still are going strong and I mop three times a week. Also use them for light wall cleaning.
much more economical than disposable. Easy to swap out pads while cleaning, all around good.
So, my method is first vacuum to remove all loose dirt, dust and pet hair.
Then, using my laundry spray bottle (good old water), I dampen sections of the floor at a time and then wet mop until one side of pad is soiled. Pad "automatically" flips to clean side. Work until both sides are soiled and then swap out dirty pad for clean and finish the floor.
That is the every couple of days damp mop. Depending on dirt level, floor gets a real cleaning with cleaner every 10-14 days.