For this achievement, you have to have sex with these 4 characters (can be in as many playthroughs as you need). To actually have sex with the character, they will either confront you in camp asking you to go to their tent or you ask yourself.
Alistair:
Alistair's conversation options open themselves up pretty well and it is easy to predict what things to say that will make him love you more. He prefers gifts like statues and runes. One gift to get him easily is his mother's amulet that you can retrieve from Castle Redcliffe in the Arl's study. You need to have him around 90% approval to get in the tent with him.
NOTE: Alistair is straight and to score with him you must play as a girl character.
Leliana
I found Leliana to be the most difficult character to score with. One good way to get her approval up is to do her optional side quest. By going through her dialogue options, eventually one will open up asking something like "I have heard that in Orlais traveling minstrels are often spies". This will start a side quest that, when completed, will give you massive points with Leliana. You can also buy her a nug in Orzammar to increase her approval. She prefers holy symbols and items of Andraste as gifts as well as shoes. Go to the Brecilian Forest and near the entrance is the flower Andraste's Grace. Give it to her for a large approval bonus.
NOTE: Leliana is bisexual and you can score with her as a boy or a girl character.
Morrigan
Morrigan is tricky because she doesn't want to be in love. Make sure to never suggest to her anything about love being necessary or good. Morrigan also dislikes when you make decisions to help people when they don't directly help you end the Blight; she hates being sidetracked. She likes necklaces and amulets as gifts, one easy one is sold by the merchant in camp called Golden Rope Necklace. Try to get her to talk about a mirror that Flemeth took from her and then go to a specific merchant in Orzammar that sells a mirror as a gift. Morrigan will highly approve of this. Bring Morrigan in your party to the Mage's tower and she will tell you of a grimoire she wants you to find. This will start up her specific sidequest which you can complete for approval points (I didn't complete the sidequest and I was able to have sex with her). You will know when Morrigan wants you to have sex with her because in camp she will tell you that it is cold in her tent and that you should come in with her.
NOTE: Morrigan is straight and you can only score with her as a boy character.
Zevran
By far the easiest character to have sex with. He starts flirting with you almost immediately after you meet him (you will get him as a party member after your first main quest mission is completed). Tell him that he is cute and such. Really, just talk to him and he will start liking you. He enjoys receiving leather gifts and precious metals. You only need Zevran to be around 60%-75% approval to have sex with him.
NOTE: Zevran is bisexual and will get with any character you make.
It is possible to have sex with 3 characters in one playthrough. I recommend starting with Zevran and ending with either Alistair or Leliana (as those are the two most difficult to have sex with). It is good to have a high coercion skill so that you can convince the next character you are going for that you aren't cheating on them with the character you had sex with previously. You will need to have sex with the last character on another playthrough. Make sure you play as the opposite gender on your second playthrough.
Lastly, here is a guide to where the gifts are that each character enjoys getting.
http://dragonage.wikia.com/wiki/Gifts