It is normal to feel sore in the aftermath of a tough resistance/weight session. However its very common to ache for upto 2 days for new exercises or when you change training method/phase.
DOMS usually peaks at around 48 hours and then subsides. DOMS comes about as a result of microscopic tears to your muscle fibres (this is considered good damage as when the tears are rebuilt by the body the muscle becomes stronger).
The good news is that DOMS won't stick around forever, the more often you train and the more your body gets used to exercise the better it becomes at repairing.
There is no one simple way to relieve the feeling of DOMS (some people including myself actually enjoy the sensation of DOMS) although some studys point to warming up and cooling down correctly as a way of minimising the effects of an intense exercise session.
Personally I find that foam rolling helps ease DOMS and recommend if you have sore muscles from DOMS to give it a go.