Below are some tips on how to make money and survive in EVE doing exploration.
Each of the starting factions has an exploration frigate (Heron, Imicus, Magnate, Probe), which is the best way to start exploring. They have the best bonuses for scanning and hacking and, with the basic fit, they will be cheap and will allow you to make a profit.
Look in the corporation fittings for the Heron exploration fitting for an example on how to fit an exploration ship. Be advised that starter exploration ships are NOT good at combat, versus players or NPCs. The goal for these ships is to go into sites that don't have any NPCs in them.
Once you get in your ship and start exploring, start in High Sec wherever you are able to scan down some signatures. You can take your time with scanning as it might seem difficult in the beggining but it gets much easier very quickly. You can also use this Scanning Tutorial. Alternatively, you can also do the first missions for the Exploration Career Agents.
Always remember to grab your Core scanner probes back after scanning; the game automatically grabs them back now, but sometimes it doesn't do it properly, so do it yourself.
If on the way you find any Data sites or Relic sites, before jumping in check the level of the data/relic sites, if they are a level I-II they should be safe. A good practice is to always warp at 100 km from the site so if it is hostile you can still warp out. Alternatively you can also use this Data/Relic Guide to check exactly what type of site it is and NPCs you might or might not encounter when you reach it.
Hacking for both Relic/Data sites has the same minigame. It's definitely more fun and rewarding then scanning, once you're done with the hacking you will be able to unlock the cargo and take what is inside. It's advised to start with the smaller cargo to hack as they are easier to get.
Use this Hacking Guide if you want to learn more about the mini-game.
Once you are comfortable doing Hisec sites, you can travel to lowsec and nullsec. If you do, use DOTLAN to figure out who has died recently in the route you are going before you go on it. Avoid systems where people have died recently. Ideally, you should travel through wormholes to get to and from Hisec.
Once you feel confident enough about your scanning and hacking abilities, you should be ready to head through Wormholes.
Before getting inside of a Wormhole, you need to first get accustomed to the Locations tab which can be found in People & Places in Personal in the Neocom. The first thing you will need to do before going inside of the Wormhole is saving a bookmark in right in front of it so you know where it is placed.
Click on the Wormhole and then right click and select Save location. SAVE THE LOCATION AS A 2-DAY “TEMPORARY” BOOKMARK in the Naval Locations' “Wormholes [Temporary Only]” folder and track it on Tripwire.
Once you've saved the location you can safely enter the Wormhole. THE FIRST THING YOU DO WHEN ENTERING A WORMHOLE IS TO SAVE THE EXIT, again as a “2-day” temporary bookmark in the wormholes shared locations folder. The second thing you should do is record it again on Tripwire.
Once you get in you will be able to see where the Wormhole took you. A few things to note down about Wormhole space would be the following:
-Before you start scanning or hacking down anything in the Wormhole, create a Safe. A Safe is the safest way to conduct activity there. To create a Safe spot you will need to warp to any far away object, planet, or star. Once you are warping when you are relatively at halfway warping to the location create a new bookmark there and name it so you can warp back to it. After you warp back to the safe spot in order to see if anyone comes for you or is around you'll need to also open you're directional scanner which allows you to scan from your ship and see any other ships or structures around. It is very easy to use and it's great practice and a great skill to develop for any pilot.
Use this D-Scan Guide on how to use the directional scanner.
If you find things/signatures in the Wormhole that you believe are not useful for yourself you can always practice bookmarks as both the Corporations and the Alliance members are always looking for new Gas sites or other type of sites to explore, harvest, or clear out. Also make sure to be aware of other sites as well. None are secure for sure if you do venture to them make sure to warp 100 km away from them.
If you do have Omega you can definitely use it for better exploration. You will be able to research the Skill for Cloaking which will alow you to use a Cloaking device on your exploration frigate. You can scan down sites while your ships is cloaked in a safe spot which will greatly increase your survival chances.