Howto convert old basement slab into finished concrete floor?
From your images it appears you're looking for a polished concrete floor. The process isn't very complicated, but it can be messy and time consuming. It's not unlike refinishing hardwood floors.

Ensure floor is suitable for polishing

Sources I've seen state that nearly any concrete floor can be polished, so long as it is structurally sound. Floors that are very porous, need extensive patching, or are wavy are probably not good candidates. New slabs need to cure for 28 days before polishing. 

Grind floor flat

 

The actual polishing consists of a series of progressively finer grinding and polishing steps. They can possibly all be performed using the same piece of rented equipment. The first, coarsest grinds (typically performed with metal-bonded cutters) flatten the floor and open up the concrete's pores. 



Densify, and maybe stain

Then a chemical densifer is applied, which seeps into the concrete, hardening its surface and filling voids, while preparing for the final polish. Around this time is when a colored stain could be applied if desired.



Polish

Next a series of progressively finer polishing grits (typically abrasive grit in a resin binder) is used until the desired level of shine is reached.