What do I need to do this?
Minimum Skills
Science 3 Prereq for Astrometrics
Astrometrics 4 Required to use Sift Probes
Racial Frigate 4 Required for your Astrometrics Frigate, and also to get a hit off sift probes.
You can do it, but you will go insane probing things out like this. It'll take you 8 minutes to get a result off your multispec, you won't have a cloak, you'll almost certainly have to drop multiple sets of quest/sift probes(at an hour a set) unless you're the type of lucky bastard that makes a living off the lottery.
For the truly masochistic, you can technically swing it with Racial Frigate 2 and Astrometrics 3, but don't expect to find anything before the heat death of the universe.
Recommended Skills
Covert Ops 4 Decreases Scan Time while in a Covert Ops Hull.
Signal Acquisition 4 Decreases Scan Time
Astrometric Pinpointing 4 Reduces probe scan deviation (more accurate hits)
Astrometric Triangulation 4 Increases probe signal strength (more frequent hits)
Jury Rigging 1 Required for Gravity Capacitor Rigs (Reduce Scan Time)
Mechanic 3 Required for Jury Rigging
Racial Frigate 5 Required for the Covert Ops Hull
You also obviously want Cloaking 4 so you can use a covops cloak, and various other skills needed to fit out the hull. You can find fittings linked off of the Covert Ops article.
To improve your scanning even further, obviously train appropriate skills to 5. You can also tack on a Sisters Scan Probe Launcher(about 45 mil in empire) for quicker scan times. If you want to go insane here, you can pick up Implants - a 'Prospector' PPH-2(150mil+) to further reduce your scan times and a Virtue set(2.5bil+) to further increase your probe strength.
Also, you probably want to do all this on an alt, and there is great 3rd party tool that will help you calculate your scan time here:
http://games.chruker.dk/eve_online/scan_time.php I could go into much more detail on it, but it's a very complex topic, and you'll learn more simply by doing it than trying to read pages and pages on it. This should give you a rough guide on how to set yourself up properly for doing the exploration probing though.