The Scan Probe Launcher I is the launcher you'll use for exploration. It's a lot slower than the Recon Probe Launcher, but it's big enough to actually hold exploration probes, which the Recon variant isn't.

The Scan Probe Launcher I uses 220tF of CPU, so you'll need a ship that can cope with this

Probes will be discussed in the next section

Covert Ops ships are excellent for exploration. They have the Astrometrics duration bonus that you also get on Eve Isk  the Signal Acquisition skill, which is extremely important for exploration. These bonuses multiply one after the other - if you have Signal Acquisition V and Covert Ops V (and you're flying a Covert Ops ship), you'll get a 0.25x multiplier on your analysis time. Signal Acquisition V gives you a 0.5x multiplier, and then Covert Ops V gives another 0.5x, and 0.5 x 0.5 = 0.25, making you four times faster than the base speed.

Three of the four races have a T1 frigate with the same bonus as Covert Ops ships, but at 5% per level rather than 10%. This isn't ideal, but it's much easier to train Frigate V than Covert Ops V. There is no Amarr ship in this role though (due to the lack of a 6th frigate), so if you're Amarr, it's either Covert Ops or crosstrain to another race for this bonus. Bear in mind that you need Covert Ops III before your Covert Ops ship becomes better than the base T1 frigate (you need Frigate V to use the Covert Ops in the first place).

The cloaking device is optional, but very useful. If you're working in 0.0, it's almost a necessity to keep you safe, but in high-sec you can ignore it if you're not at war with anyone. As you can't warp while analysing, the Prototype or Improved cloaks will do the job ok, and cost a lot less to boot.

The Gravity Capacitor Upgrade I rigs do another -10% duration each, for a further 0.8x multiplier on your scan time with two. This takes you down to 0.2x total modifier with max skills, which is not to be sniffed at

You will, obviously, need the ships and kit to deal with the sites you find. Combat sites need combat ships, mining sites work great with barges, while profession sites need a ship with the appropriate modules fitted - Analyzer and Salvager for Archaeology/Salvage sites, Codebreaker for Hacking sites. You can fit these on your Covert Ops, but this will usually mean someone else coming along in a combat ship to clear the place out first. Generally I put my profession modules on my combat ship, because I prefer not to risk the Covert Ops unless absolutely necessary