Here is a rough order that I'd look at:
* Go do the Advanced Tutorial Agent for Exploration; mess around with the ship and scanning interface. You want to build up familiarity with the procedure in high-sec before you go to null/jspace.
* Set up a skill plan for scanning; you eventually want: Archaeology V, Astrometric Aquisition/Rangefinding/Pinpointing IV, Astrometrics V. Its okay to work on these in increments; the first to V should be Arch so you can equip a Relic Analyzer II. I omitted Hacking because I don't even run that module; it used to be that Data sites were garbage... I've heard that CCP buffed it but it still seems like a waste of time to me.
* Set up a skill plan for ships. The rough order of progression for explorers are: T1 frigates (each race has a frig specialized for exploration) --> Covert Ops --> Astero/Stratios --> T3. Really, flying a cov ops is fine for making fat stacks of isk. Progressing further means you can kill other explorers; or for T3s, you could run some combat sites too. They're also much more expensive which skews the risk vs reward. For what its worth, I've been exploring for over a year and still use Cov Ops. I'm finishing off a scanning skill to IV then going to build up my drone skills to jump into Astero soon.
Preferably, you will be flying a Covert Ops with Cov Ops Cloaking Device (requires cloaking IV) before you leave high sec. That isn't necessary, it just makes operating in jspace/null far easier. If you get antsy and feel comfortable scanning and moving around you can always roll out in your T1 frig just for practice, make sure your clone is cheap and who cares if your 2 mil ship dies.
This should be enough to get started on over the next week or two. You want to feel exceedingly comfortable entering a system, dropping probes, warping off safely (cov ops cloak or MWD/cloak trick, google it), scanning, and collecting loot while monitoring Dscan (i.e., press dscan every 3-5 seconds). Note: many null systems are empty which means you don't have to be nearly on-guard.
If you get into it, I can take you on a null or jspace jaunt.