waivers
 

Can someone please explain how placing a player on waivers will affect the teams salary cap? I'm guessing the team would still have to pay out his remaining salary for however many years are left in his contract, but I'm not sure. I have looked on the internet and I can find how waivers are done but I cannot find anything about how making any kind of roster moves affects a teams budget. I even got on amazon and looked for something about the money business of baseball or a beginners guide to baseball agents and came up with zilch.

The team is still responsible for the players salary.
You are asking 2 questions though.
1) How does it affect a teams salary cap. This is an OOTP fictional league question because MLB does not have a salary cap. I am pretty sure OOTP includes all salaries, MLB and MiLB to figure the teams payroll.
2) In real MLB the team will be responsible to play the player unless another team claims the player. Then they are on the hook.

so if I had the guy signed to a three year contract and another team claims him off waivers they will pick up his contract and I will no longer be responsible for it? And if he clears waivers, how will that affect my budget? (We have a 95 million cap in my online league)

If he clears waivers your budget will be unaffected as the player remains on the payroll.