The first thing you will want to do when you enter The Abyss is turn in your quest to Michalis. Accept the followup and head to the "X" on my map.
Here you will want to speak with Eulos. He will send you into the ring just south of him. Here you will need to talk with each of the NPC's in clockwise order, watch their cutscenes and accept the quest to talk to the next NPC. Wether or not you want to watch these cutscenes is up to you. They just explain The Abyss.
After you watch all these cutscenes if you're still curious about The Abyss feel free to take a look at my Abyss Guide.
After you complete The Abyss Walkthrough you will want to fly north to Claudia to turn in your quest. Just hit "M" and look for the only dot on the map in Terminon Landing. Speak with Claudia and turn in your quest. Now, It's time to get to buisiness, leveling. The first place and one of the safest places for you to level at 25 is the Western Shard of Latesran. all around the outside of this island you can find Golems that are level 25.
On the inside of the island you will find teleporter NPC's that will take you to The Upper Abyss. The Golems here will take you to level 26 easily.
When you reach level 26 you will want to go just north of the Western Shard of Latesran and kill the mobs up here. These mobs are level 27 and they will easily take you to level 28.
Once you reach level 28 you will want to head east of Teminon Landing to our next area.