Welcome back; you will find that a lot has changed in the game over the past few years.
You can find details about Abyssea at http://wiki.ffxiclopedia.org/wiki/Category:Abyssea
To start Abyssea (assuming you have the expansions) you will need to talk to Joachim in Port Jeuno (above the AH). Abyssea entry is granted by traverser stones, which, at the beginning, Joachim will give you one of per day; each stone allows you to remain in abyssa for 30 minutes. As you progress, you will accrue stones faster, and they will allow extended stays; in addition, you will be able to get time extensions while in abyssea.
It is best to start the storyline with Joachim, then wait a few days to build up some stones. During this wait time, you can also run around the world finding the Maws that you enter abyssea through; you will get a quest on the first entry to each maw. Experience in Abyssea is typically party based... Abyssea mechanics are different from other aspects of the game, and partying in alliances can generate exp very quickly. Typically, you can go to La Theine, just east of where the crag was and find a large quantity of people exping there on worms; put your flag up and/or ask nicely, and you will probably quickly get invited to the group. All jobs are useful in Abyssea, so you don't have to worry too much about job selection for exp there, although anything under 75 will not be useful for you at the start (there are roles lower level characters can play there, but that will require some previous experience).
Also, as you are returning, you will also want to start the Voidwatch mission line http://wiki.ffxiclopedia.org/wiki/Category:Voidwatch
With this, you don't need to worry too much about doing anything other than what the page lists as "First Step", however, as Voidwatch is another event that gives an item to participate once per day, starting the process now will allow you a lot of runs when you are ready to start participating in that content.
In the interim, you can also do GOV in Crawlers Nest and Bos[tab] before entering Abyssea.