The Café is a new community project offered in Animal Crossing: New Leaf, which is a replacement of Brewster's from previous Animal Crossing games. As with most other community projects, it must be unlocked before being available in the list.

Unlocking the Café

After building the museum expansion, the café can be unlocked after seven days, if there are fifty items total donated to the museum, with at least one donation to every type of exhibit. One the conditions are met, the mayor must talk to Blathers, who will then suggest building a café for his friend, Brewster. After this, the café will appear on the list of public works projects. Brewster's Café costs 298,000 Bells to construct, and it is a permanent building - it cannot be demolished or relocated so choose the site carefully.

Using the Café

Players may order coffee from the Brewster, who runs the café, for 200 Bells once a day. After the 3rd cup of coffee, the Brewster will offer the player "to go" coffee, which can be drunk outside the café. Five sips can be taken before it being completely consumed. Occasionally, villagers or some special NPCs can be found at the café drinking coffee.
Here are the special NPCs and the time when they may appear.
Special character
Time
Pelly or Pete
6:00AM - 6:55AM
Tortimer or Shrunk
8:00AM - 9:30AM
Mr. Resetti or Don Resetti
12:00PM - 1:30PM
Kapp'n or Phineas
2:30PM - 4PM
DJ KK
5:30PM - 7PM
Phyllis or Digby
9PM - 9:55PM
Gracie, Kicks or Tom Nook
12:00AM - 1:30AM
After unlocking part time job, Brewster may ask what kind of coffee beans, amount of sugar, or amount of milk the player wants in their coffee when ordering inside the café. This only affects the dialog that appears after drinking coffee.

Part time job

After ordering coffee eight (?) times, the Brewster will offer the player a part time job which can be started the next day. When working at the café, a total of three villagers (may include one not from your town) and one special character will come in to place an order. You only get a partial order and you must figure out the type of coffee beans, amount of milk and spoonfuls of sugar for their order. Each character has their preferred coffee combination. After getting a character's order correct, they will start to ask for "the usual." Brewster keeps tabs on your progress and you are rewarded for correct orders. For 1 correct order, you will receive "plain coffee beans" (sellable for 500 Bells). For 2-3 correct orders, you receive "good coffee beans" (sellable for 1,000 bells). If all four orders are correct on your shift, you will receive "superb coffee beans" sellable for (2,000 Bells). The beans you receive can be sold for the amount in parenthesis. After serving a certain number of correct orders over a period of time, Brewster will reward you even further with Café Furniture items.
Note that on holidays and other event days, you might not be able to work part-time at the café.
(Click here for the coffee guide)

Here is the list of items received after serving a certain number of coffees:
Reward item
Picture
Coffees served
Sell price
Coffee maker

16
200
Espresso maker

32
125
Siphon

48
445
Coffee cup

64
500
Milk and sugar

80
250
Coffee mill

96
400
Café uniform

128
108
Brewster gyroid

160
192
224
255
828