How should I polish my concrete basement?

My basement is finished with carpet and vinyl tile, but I want to pull it all up, and polish the concrete. I know that there will be some residue of glue from the tile, and matting from the rugs where there was water damage, but I was wondering if there was a way to remove it without renting a grinder. I was doing research, and an overlay sounds good or an epoxy. I also want to dye it. How do I go about this?.