You select the proper approach and make SURE you have the NAV/GPS switch to GPS!
Since I'm not familiar with the garmin's (hey you don't find those in the 737's

) I cannot offer you any further advice other than YES, if it's a GPS approach you should be able to fly the approach by using the GPS as the only nav. source.
Billerator (this is long, sorry!) RNAV and GPS is not the same thing. RNAV has to comply with some strict navigation standards.
You don't need a GPS to fly in RNAV, just make sure radio updating is available.
The GPS is not needed because the FMC doesn't only use GPS for position updating, but also DME-DME, VOR-DME or even the IRS of course...
RNAV allows for a more tightly controlled airspace, some as narrow just some nautical miles. RNAV capable aircrafts will have better treatment in both cruising altitude and routing, but the price is quite high. We're talking about expensive gear here

To fly RNAV departures/approaches the aircrafts must meet a criteria called RNP. RNP is short for Required Navigation Performance. RNP is the navigation capability which is necessary for the aircraft to fly in a certain airspace segment.
RNP is expressed in nautical miles so if it says:
RNP 1.0
it simply means your navigation has to be more precise than a 1nm error from your true position
Different air segment has different RNP values. Oceanic airspace where accuracy is not that important allows for a 12nm error margin (RNP 12) but in busy airspace such as during an approach the RNP is 0,5!

These values are defaults and are subject to change.
All segments allows for a 400ft vertical error, forgot to say that.
Okay we now have the RNP values, but how do we know we can trust our Navigation instrument?
The answer is ANP! ANP is the aircrafts Actual Navigation Performance, so by just a quick glance on the FMC (LEGS and POS SHIFT pages on the Boeings) you can see the RNP and your current ANP. If the actual performance is greater than the required performance (ie ANP is a greater value than RNP) you'll have some nice warnings

I know many people confuse GPS navigation with RNAV, so I'm just trying to point out the differences.
I'm surprised I even remembered all this