There are two main ways to expand a counter: by adding more counters, or by linking multiple counters together.
Adding more counters is the most straightforward way to expand a counter. This can be done by simply adding more of the same type of counter, or by adding a different type of counter that interacts with the original in some way. For example, if you have a creature-based deck in Magic: The Gathering, you might add more creatures, or you might add artifacts that help creatures survive or deal more damage.
Linking multiple counters together is another common way to expand a counter. This can be done using special abilities or spells that allow two separate counters to become one (such as combining two +1/+1 counters into a single +2/+2 counter), or it can be done using card effects that move counters from one place to another (such as moving all your +1/+1 counters from one creature to another).