Each section will start with a bullet list of the steps you need to take, and then will explain each step

Skills

You will NEED:
- Astrometrics IV
- Signal Acquisition I

You will WANT:

- Covert Ops
- Astrometric Triangulation
- Astrometric Pinpointing
- Signal Acquisition

As high as possible
Astrometrics IV is needed to use all the probes properly. You can succeed with level III, in theory, but it'll be very hit and miss (mainly miss).

Signal Acqusition I (or some other bonus that has the same effect, see discussion on ships and rigs shortly) is needed to prevent your probes from expiring before you finish analysing them.

Covert Ops ships give the same bonus as the Signal Acquisition skill, and is therefore by far and away the best ship type for exploration. The bonus increases per level of Covert Ops, so the higher your level, the better.

Astrometric Triangulation increases the strength of your probes, making them more likely to find something in the first place

Astrometric Pinpointing reduces the scan deviation of your probes, making them more accurate

Signal Acquisition reduces the amount of time it takes to analyse a result, and thus the amount of time it takes to find a site

Additionally, you will need the skills to make use of the sites you're looking for. If you're after combat, have a good combat skills, and ideally some friends. If you're after mining, look up the mining guide here. Profession sites require either Archaeology and Salvaging, or Hacking. The higher these skills are, the faster you'll be able to loot the site of valuables. Gas Cloud sites are a special case that will be discussed later.

Equipment

You will NEED:
- Scan Probe Launcher I, with a base analysis time of 600s (10 minutes)
- A ship that can fit said Launcher (does not require a launcher hardpoint, but does need to be able to handle the CPU load)
- Some probes (see later for exactly which ones you'll want)

You will WANT:
- A Covert Ops ship - the one with the Astrometrics bonus, not the Stealth Bomber variant
- Failing that, a T1 Frigate with the Astrometrics bonus (none for Amarr, sorry)
- A Covert Ops Cloaking Device II for your Covert Ops (for safety in low-sec/0.0)
- A pair of Gravity Capacitor Upgrade I rigs
- Ships and equipment to deal with the sites you find