Now that you've hived your bees, you'll want to check on them weekly to be sure that the queen is alive and laying eggs. You should be able to find eggs, larvae and capped brood while checking for mites and other pests. Here's some great information and graphics on what you should and shouldn't be seeing.
What You Should be Seeing
The Queen - She is the largest bee in the colony with a long slender body. She is responsible for laying all of the eggs. Without eggs and brood, the colony won't survive for very long. Some beekeepers choose to mark their queens with a small dot of paint so that she can be spotted easily.
Eggs - The eggs are very small (only about 1.7 millimeters long) and tend to look like a grain of rice at the bottom of a cell. The best way to spot an egg is to hold the frame up to the sunlight. The queen will only lay one egg per cell. Being able to spot eggs within a hive is one of the most important jobs of a beekeeper. It is the best way to ensure your queen is alive and well.
Brood Cells - Three days after the queen lays the egg, it will hatch into a larva. Healthy larvae are white and resemble small grubs curled up in the cells. They will grow quickly, shedding their skin five times. Within five days, worker bees will cap the larvae cell with beeswax and then the cells become known as "brood cells". It is at this time that the larva becomes officially known as a pupa and over a period of 12 days fully develops into an adult bee. At the end of this 12 days, the pupa will chew through the thin layer of beeswax to join the other members of the hive.
Honey Cells - The bees will start to gather and harvest nectar from nearby flowering plants. They will begin to store this nectar in the brood box around the outer edges of the brood frames. Once the cell is completely filled with nectar, it is dried and then sealed with a thin, smooth layer of beeswax.
Pollen Cells - They will also start to gather pollen collected from nearby flowering plants. They bring this pollen back to the hive and store it again around the outer edge of the brood frame. Typically, you will find a ring of pollen cells around the brood cells and then the honey cells will form an arch around the pollen and brood cells (near the top and edges of the frame). The bees will use this nectar and pollen to feed the brood.
What You Shouldn't Be Seeing
Queen Cells - Rough in texture and about an inch in length, it sort of resembles a peanut shell. These are very important to keep an eye out for. The formation of a queen cell means that the colony is getting ready to swarm. If you see a capped queen cell, it's normally too late to prevent them from swarming; they've already made up their mind.
Too Many Drone Cells - Drones are the male bees within the colony. They normally appear in late spring and are the result of an unfertilized egg. Their sole purpose in the hive is to mate with the queen. They are larger than worker bees, have a round abdomen, large eyes, and no stinger. Some drones in the hive are completely normal. It is when you get too many that you have a problem. Too many drones in the hive means that your queen wasn't mated properly and is only laying unfertilized eggs. Drone cells are easy to recognize. They are domed and larger than worker bee cells. Typically, they are grouped together on the outer edge of a frame. If you find that the middle of your frame is composed of drone cells, most likely you have a "drone-laying" queen and she'll need to be replaced.