As the general-purpose assault class of Team Fortress 2, the Soldier is easy to pick up and play but difficult to master. The Soldier is durable, capable of both long range and close quarters attacks against enemies and buildings alike, is quite accurate, and can often access places on various maps others cannot via rocket jumping. However, he is slower on foot in comparison to most classes, and can pose a threat to himself at close range due to potential self-damage. Regardless, the Soldier is a solid "blast 'em everywhere" class, and experienced players can assault or defend key strategic points with ruthless efficiency.

Quick Tips

Always take the high ground. You're harder to attack at higher elevations, and your rockets are harder to avoid.
You can try rocket jumping to help get to over or at the same level as the enemy.

A team without Soldiers is probably offensively weak. Fill the role to push back the other team and accomplish the objectives.

Switch over to your secondary or melee weapons at close range to prevent point-blank rocket explosions from hurting yourself.

Look for rocket-jump shortcuts, especially in Capture the Flag and Control Point gametypes. A simple backcap can take an entire team by surprise.
Memorize where the health packs are on each map, as rocket jumping costs a significant fraction of your health.

Try to anticipate where your enemies are going, as your rockets move relatively slowly. Juggle opponents by shooting your rockets below their feet and launching them into the air for a predictable follow-up shot.
Changing to your Shotgun can be useful for taking out quick-moving targets like Scouts, as its bullets instantly deal damage.

Avoid directly shooting rockets at Pyros who have a habit of airblasting. Fire rockets beside them to safely deal splash damage, or bait them into wasting their airblast first, leaving them vulnerable. Better yet, use your Shotgun against them.
When fighting Pyros, don't fire rockets as fast as you can; they may predict when you'll fire the next rocket and reflect it. After firing, delay firing the next shot in order to confuse the Pyro.

General