If you are looking for a little more excitment than just killing rats, plus better loot bounties usually, head to a deadspace complex. (see chapter 11 for deadspace strategies and locations) You can think of these as dungeons or instances in space - an area where warp does not function normally (though you can usually warp to a "safe" planet if you need to once inside) and you need to go through acceleration gates in order to progress from "room" to "room"

These provide a greater challenge than just grinding rats, tend to have at least some story line included with it, may have a mission attached to it providing even greater rewards, and you will find all kinds of bounties and loot inside. It is possible to make more Eve Isk running deadspace complexs than any other rat strategy, though it is a larger time commitment and often a much higher risk to your ship. (Remember, rats will not pod kill you, so you are only risking a ship in these areas, unless you run across a player who does not want the compitition inside.)

Of course, if this all seems to be too much hassle, you can just skip those steps and buy your  Eve Isk right away. However, when you do, be sure to check reviews and compare prices in order to make sure you get a good deal.

Another method we just breifly touched on is missions. When you are a new combat player you will probably want to run a lot of these, as they are at level 1 usually pretty short and have a decently high reward, not to mention pointing you in the right direction for hunting rats more often than not. However, the missions do not scale in EVE terribly well, so watch the local and corp channels for people complaining about particularly difficult or not worthwhile missions, and you may save yourself a ship or two.

Story line missions tend to be a lot more fun, plus will earn you large faction increases and generally more Eve Online Isk. (a mission will be clearly marked as storyline in your journal, as well as tell you how many more story line missions are in that particular line)

Level two and three missions get progressively harder, of course, but the best ones start becoming available at level 4, where you can earn a large amount of  Eve Isk and will usually have a lot more fun doing so. If you enjoy doing missions at all, suffer through the 2 and 3 levels to get to 4 and up, it is worth it once you get there.

Should you prefer to earn  Eve Online Isk the traditional way, you will find this EVE Online guide to be a great help. It offers advice on various ISK-making methods and provides a lot of general hints for newbies and veteran EVE players.