I have 2 beams that I constructed out of 3x10s (three thick and spanning 23 feet). I am using these to support my springy floor. The house is a 1970's backsplit and the space they are in is a 4 foot high crawl space with a cement floor.

How do I raise these up to place the support posts under?
I have thought of 2 ways, but need some one to give me the safest way to do this by myself.
1. rent a large car jack and raise it that way.
2. some kind of pully system.

Please help, as I need to get these up before I can start tiling my entryway and kitchen.

Definitely no on the pulley idea followed with a close second no on the car jack. You need something along the lines of a 20 ton bottle jack and plenty of support spread out on the floor to prevent cracking. "2 beams that I constructed out of 3x10s (three thick and spanning 23 feet" did you have an engineer or architect give you the load requirements? First off I have never seen a kiln dried 3x10 in 50 years so maybe we're not using the correct terms. If you have a cement crawl space you'd be better off and safe by creating several smaller points to carry the load. You can buy adjustable metal columns for this purpose. Safer, better, cheaper than trying what you have in mind.

We Just Done A Job Like This, Except We Didn't Have A Concrete From, So Your In Good Shape And Actually This Job Shouldn't Take All That Long, Id Say 4 Hours Tops If You Have 2 People. And You Do Need That

First Off Buy You A 4 X 6 X What Ever You Can Handle Comfortably
Like Ballanger Said Use Some Metal Post Jacks. These Are Adjustable .
What Id Do Is Get 3 10'ers And Put One Up At A Time , Both Of You Should Be Able To Hold The Beam While You Getting The Post Set, My Advise Is Go Ahead Get The Post Out And Set It At The Right Height Where There Is Little Adjustmetn To Do, After You Install The Beam And Have The Post Under It You Need To Go Back And Fasten The Beam With 3" Screws To The Joist And Then Fasten The Post To The Beam With Some Screws Also.

If There Is A Sag In The Floor You Will Need The 20ton Jack To Temp Hold The Floor In The Right Level. To Check To See If You Do Need To Do This , Pull You A String Along The Bottom Side Of The Joist And Just See If You Have Any Low Spots