A cement based adhesive.
Cutting, you will need a diamond wheel, preferably, although they can be scribed and snapped for straight cuts. In which case a rough file for tidying up edges.
Grout lines, your choice of spacing. Usually 1/4" on flooring.
Finishing. I used to use HG Green polish. Now known as HG Impregnating Sealer followed by Golv polish. Now known as HG Satin Gloss Polish.http://www.tilefixdirect.com/category/h ... tAod430nSw
If you are going for a ready sealed type of tile you can ignore the polish info above. Those are for unglazed tiles.
You might consider a floor levelling compound if the substrate is more uneven than can be taken up with the adhesive. Something like this. http://www.diy.com/nav/build/building-m ... g-10487625