What is the easiest way to fix a loose chain? Are there adjustments that can be made instead of replacing it?
It depends on what you mean by 'loose'... Chains stretch naturally over many hundreds of miles, and the stretching of the links is actually a good indicator of wear.

If, instead, it seems like there is a lot of slack or 'extra' chain, this is an indicator of one of two issues:


The chain is simply too long. All new chains (not already on bicycles) come longer than they need to be. If you recently replaced your chain, and didn't remove the extra links, this would cause the chain to be loose.
The dérailleur is not creating chain tension. If you find that the chain seems to sag at both the top and the bottom, this may mean that your dérailleur has lost some of it's 'springiness' and is not effectively creating chain tension. It's hard to determine without further details, but if this is the case, the dérailleur may need to be replaced.