Some spoilers below:
I'm assuming you mean reaching the dinner with Reth, as that seems to feature the most Reth-related content.
Starting a fresh game, choose whatever until you reach the question "Tell me, what else do you desire?". Do not choose 'Love'. This will boost your charisma by two points, and you need to have ten (the default value) when you meet Silas.
The next question will have two options that grant charisma. "A lover" and "Friends" both grant one charisma apiece. Those will leave you with eleven charisma, so do not pick them!
Choose whatever until you reach reach Silas. As stated earlier, lie to him when he asks if you are going to the academy. If it interests you to know, you get one charisma point for lying to Silas so you now should have eleven. If you had twelve at this time, he would give you a ride.
The time that you spend with Alderic doesn't seem to affect any interactions with Reth, so choose what you want during his phase of the game. Eventually you'll meet up with Silas again and get a ride to the academy, where you can choose whatever last name and major you want. Orion will drag both you and Reth to the academy tour, where you will have the option to ask about the room with the large black pots. Do choose to "Ask Reth". This is your only opportunity to get the needed favor from Reth.
Take any choice until you reach the showers. Do not peek at Reth! You won't even be able to ask him to join you at dinner if you do. If you successfully resist the urge to see naked hyena, and did get the two points of favor by asking him about the room, while drying off afterwards your character will automatically invite him to eat with you.
Unfortunately, right after the dinner is also the end of the current build, so there isn't much to Reth's route. Hopefully this will be expanded in the future.
By the way, if you initially choose to tell Silas the truth you can still get some favor from Reth by selecting "fight back" and choosing to ask him questions during the tour. However, you won't get the scene with the shower nor invite him to dinner. You will get the option to have him guide you to the admin office, but this will lose you favor with him.