The number preceding the "/" tells you how much damage will be reduced. Whatever comes after the "/" is the attack type that completely bypasses the DR.
DR 5/good or silver (found on imps) subtracts five points of damage from weapons that are not either good-aligned OR silver. Those weapons you carry in case of encountering a werewolf will do just fine here. Your Holy steel, cold iron, or adamantine weapon of choice will also bypass this DR.
DR 10/magic and silver (found on vampires) will subtract ten points of damage from weapons that are not both magic AND silver. Casting
magic weapon on the stuff your party normally carries for fighting werewolves will solve this issue.
DR 15/magic and bludgeoning (found on liches) can be a hassle unless you've got a magic warhammer (or the like) handy. If you're stuck using a greataxe or bow, you may end up doing little or no damage.
DR 15/good and piercing (found on rakshasas) is pretty nasty. If a paladin casts
bless weapon on his longbow or spiked chain, he can enjoy some good success against rakshasas. The classic rakshasa-slayer is a holy crossbow, and in 3.0 a hit from a holy crossbow bolt spelled instant doom for the fiends. 3.5 did away with that vulnerability but toned down their DR to compensate.
Energy resistance is a bit more straightforward. If an attack is of a particular energy type, simply subtract the resistance amount from the amount of energy damage.
If someone hits a
tiefling (Resist 5 to cold, electricity, and fire) with a flaming weapon, they will do normal weapon damage plus 1d6-5 fire damage. It is still possible for the tiefling to take a single point of fire damage from a flaming weapon, if the attacker is lucky.
If someone uses that same flaming weapon against a
vrock (fire resist 10), they won't be getting any bonus damage from their flaming enchantment. The demon coincidentally also has DR 10/good, which can cost the attacker even more of their normal damage potential.