How do I get more retainers?

There are a number of ways to get additional retainers, so I'll list them here from easiest to hardest:

1. Level Up. As you level up (by gaining prestige and earnings), you will also sometimes unlock new retainers. To find out what you get on your next level up, click your portrait in the upper left corner and then click Preview. You can see that what your next upgrade reward will be (either a retainer or a beast, usually).
2. Retainer Cards. Collect retainer cards (or fragments of retainer cards, which you can then merge) from events, Lucky Draw, or by buying them in Exchange Shops. They can then be exchanged for retainers or beauties in the Lucky Draw Exchange Shop. And, once you've purchased all of the beauties/retainers there, you can then use any retainer cards to upgrade a retainer's Talent, making them more powerful.
3. Recruitment. In the suburbs, under Recruit, you can see an area with a bunch of potential retainers and beauties. To recruit them, you will need to collect a certain amount of items. The easiest to gather are tokens for Pathfinders and Grandmasters (requiring only 20 to unlock), which can be purchased in exchange shops, earned in the Infirmary, won during events, etc.
   
   More challenging to gather are event-only tokens such as for King Yama (via Ghost Market), Grand Chancellor (Wise Strategy), and the rest of the Masterminds, etc. It will take a number of events before you can possibly unlock these as you need 100 to get a retainer, though the higher you rank in an event, the more tokens you will receive.
   
   Also of note is that you can get Jade Fragments to unlock Beauties of Qinhuai -- the difference with this is that all of the beauties can be unlocked with any jade fragment; when you merge them, you have to select which type you want (Verdant Jade, Dream Jade, etc.) You will sometimes collect a particular type of jade during an event (for instance, the Restaurant C.S. Event offers Empyrean Jade) or the jade fragments (as in the Feast C.S. Event). The great thing about these beauties is that they are both beauties AND retainers.

Ultimately, it is a game of patience and collecting. You can speed things along by making purchases and there are some events in which it is basically impossible to earn the related retainer without doing so, but it isn't necessary to do well in the game to unlock them.