As for when to replace the chain, the answer is before it wears out. Invest a few dollars in a chain wear measurement tool and check it (and all your chains).
Adjusting the eccentric is a matter of the specific design. Most have 4 (2 each side) locking set screws. Losen all 4 and use a pin spanner to rotate the eccentric to tighten the chain. I prefer to use a bottom bracket wrench to turn the eccentric but it only fits on 2 of my bikes.