I got really, really, bored, so I decided to make this.

Build the Cartographers Guild.

What's the point in catching wild pets if you don't know where they are? Yes, there is an Inn guest that can help you, but the Cartographers Guild is permanent. This increases the chance of catching a wild pet.

Well, that's the only thing I highly recommend. But here are the tips.

Tips:

Do not place your catchers where the wild pet is. The wild pet will move to an adjacent area, so place your catchers in an adjacent area. This usually happens for me, but it isn't guaranteed.

If you don't want to waste you vermillion on a pet that has bad genes, or if you don't like bad gene surprises, you can check if the pet has bad genes before the taming is finished by looking at the tactics for negative maneuver.

Invite the Druid. The Druid will permanently increase the pets' stats by 10%.

I know that was really, really short, but if you want me to add something, post your suggestion here.

Lol, you might want to read this: http://beastkeeper.com/thread/5218/1#43168

Though I didn't know: Invite the Druid. The Druid will permanently increase the pets' "better gene rate" by 10% every time you invite him. -- From the wording, it seemed like every time you invite a Druid, he gives you a +10%, meaning, +20& for inviting a Druid twice. Did I get this part correctly?

I took it to mean the pets caught while you have a Druid have a 10% guaranteed boost to all stats. For example, a pet whose base Constitution would ordinarily be 40 would now have Constitution of 44. And I'm pretty sure the bonus doesn't stack for inviting multiple Druids in a row, because that would make it far too easy to abuse. It also wouldn't really make sense, because all of the other invites are only effective during the 1-3 days their visitor is in the Inn.

Yes. Sumatra_Echo is right, the Druid increases the stats a pet will be caught with by 10%.

And yes, you only get the bonus of the Druid while he is in your Inn. So since he leaves after 3 days and that's the earliest you can get a new Druid to visit you, you will never be able to get a 20% bonus from Druids.

If you use an extra invitation, you replace the old one. Like, if I invited a Geneticist and then realised I'd rather have a Trainer, I could use a Trainer invite on top of the Geneticist invite. The next inn guest would then be a Trainer instead of the Geneticist. I wouldn't get the first invite back though, so my Geneticist invite would have been wasted. In this current case, this means that I can only invite one Druid at a time and thus still only get a 10% stat increase.

I do understand the stat increasing thing, but after I invited the Druid a couple of times, the genetics weren't as bad as before when I caught wild pets.

Oh, and Timain, are you saying that after the Druid leaves, there is no boost anymore?

I am really new and don't understand this: 

"if you don't like bad gene surprises, you can check if the pet has bad genes before the taming is finished by looking at the tactics for negative maneuver."

Some genes give a pet different maneuvers (attack maneuvers,movement maneuvers,defence maneuvers and negative maneuvers).

Here's the list with all maneuvers and their required genes:Maneuvers