I need server A to be able to reach server C (a mail server). server B can already reach server C and server A can reach server B. Is there a few simple steps I can take to add a static route to server A to solve this?
No, at least in IP space.
If they aren't on the same subnet (xxx.yyy.zzz.1 and xxx.yyy.zzz.2) the two computers will require a router to connect them. If they are on the same subnet then a switch is all that is required.
Given the simplicity of you question means we're guessing blind, I'd first recommend that you check to see if A and C both have a "default gateway" that matches an IP of a local router for each of their subnets. And I'd check for firewalling (both software and hardware) at the same time.
Now A should be able to interact with C, and vice versa.
(Warning: route syntax above is from Solaris, because that's what I have historically spent most of my time with; linux and windows routing is done slightly differently. Also, making all these changes permanent across reboots is left as an exercise to the reader.)
As others have said, more information is needed.
If Server A is Windows you can try:
however it's likely that the three servers are on different subnets, which means this won't work...
In that case you will need to do something about the router / switch configuration.