Your muscles get sore from a buildup of lactic acid that causes damage to your muscle cells. To minimize this you just need to put in as much cardio as you can after your strength training workout. This gets your blood flowing and flushes the lactic acid out of your muscles where your liver filters it out before it causes as much damage.

Plan your workout to accommodate a transition to focused strength training. Start with muscles that heal quickly, specifically core, calf and forearm muscle exercises. These muscle groups contain smaller muscles that are able to heal fast, but most importantly are required at some level or another for working out all other muscle groups and you want them to be strong and conditioned before you try larger muscle groups or risk injury to these smaller weaker muscles.

Interval training seems to provide the most benefit for me. You gain real power and endurance instead of puffy useless muscle. The muscle that I put on is much denser and stronger, and the overall level of pain is low compared to body building style muscle isolation workouts. I do sets based on time, not reps (though I keep the weight high enough to make it hard to keep lifting for the whole time) and have 30 second or less cool down periods between sets. I drink lots of water between sets. I always end lifting with combination exercises that work multiple muscle groups together including my focus group for the day. This improves balance and coordination. The last thing I do is run 2 miles as fast as I can, then slow down to about an 8 mph pace and run until I run out or either time or energy. This seems to flush out my muscles pretty good, and adds the endurance part to the workout.

Big picture:

-Warm up and stretch thoroughly
-Drink lots of water
-Work up to working out starting with core and support muscles first
-Finish with cardio so that you flush out the lactic acid
-No pain = you're not doing it right.