DR is a straight reduction of damage. It includes a number and a list of what attacks break it. So DR 5/silver means that all damage is reduced by 5hp unless the damage type is silver. Arraetrikos has DR 15/silver+good on Normal so the base damage you deal to him is reduced by 15 unless your weapon has both the silver
and good properties. DR 10/- means the target has 10 reduction to all melee damage and it cannot be bypassed.
Mobs can have DR to all kinds of things. Weapon material (silver, adamantine, cold iron, etc.) Weapon type (slash, blunt, piercing). Or even DR to non-magic weapons.
It's simple to know exactly what damage type each weapon does because the weapon detail window lists it. People constantly say things like "Oh, I didn't know flametouched iron did good damage!" If they would have opened up the weapon's description, they would have seen it called out explicitly. Here's an example:
This weapon does 1d8+1 damage of the types Slashing, Good, Lawful, and Magic. So it would bypass DR that includes those types. Would it bypass Arraetrikos' DR? Nope. Because it doesn't have the silver property, and Arraetrikos has DR 15/Silver+Good, all damage it delivers would be reduced by 15.
As far as getting high DR, it's not easy for rogues. Some classes have natural DR but rogues don't. Stoneskin is probably our most common way. You can purchase Stoneskin wands and use them even if you don't have great UMD yet (They can also be used on party members...yet another way rogues can help). Most melee characters eventual get a Mineral II item or two (or three) and each of those comes with 2 clickies of 15 minute, 150hp, DR 10/Adamantine. That's a pretty nice buff for most quests.