Another method is to purchase commercially raised bees. Each of these brightly colored boxes is called a Nuc. They will have approximately 5000 bees in each one. 

Advantages:

• They are usually gentle

• Are already established

Disadvantages

• Expensive

• Usually have to drive long distances to purchase

• Theses are some hives I recently purhased. They were quite full of healthy bees and an egg laying queen.

• The queens in these boxes are marked with a paint pen making them easier to find and the color they are marked lets you know what year they were introduced into your hive

Capturing wild or feral bees is one approach to expanding your apiary. This picture is called a swarm which usually happens when I hive gets too full and they need another home. 

Advantages:

• They are cost-free.

• They exhibit greater resilience, having already adapted to surviving in the wild.

Disadvantages:

• They tend to be more aggressive and may include Africanized bees. Introducing a queen from a gentler breed can help mitigate this behavior.

• This method requires time and patience.

• I purchased these queens to help gentle my hives. I have two hives with aggressive bees that are very protective of their hive.

• Inside each box is a marked queen with her attendants. The attendants keep her fed and protected.

• These bees are Italian Hybrids, known for their gentleness.

• Unfortunately, to introduce new queens, you must first locate and remove the existing queens in the hive. Otherwise, the new queen will be killed by the other bees, as they perceive her as an intruder. Each hive can only have one queen. So we had to find the queen bee out of a hive containing 10,000 bees. Not easy.

This is a swarm trap I built and hung in a tree. Inside, you hang frames for the bees to create comb on. To entice them, you add some old comb that has that "bee" smell. 

Also, you add some Lemon Grass oil because the scent a queen gives off smells like Lemon Grass. This fools the scout bees into thinking there is already a queen in box. 

After the scouts found their new home they summoned the queen and all her workers. Soon  they are filling up the box.

One last method is to take a healthy full hive that you already have and split it. Beehive splits are a beekeeping technique where a single, strong colony is divided into two or more smaller colonies. You will have to furnish a new queen for one of the splits or you can let them raise their own.