Skill checks are made using 3d6 instead of 1d20. Rules for taking 10 and taking 20 still hold as before. This makes the skills more reliable, and makes spectacular success and spectacular failure much less likely; rolls of 1, 2, 19, and 20 are now impossible.
This applies to any check that would normally be 1d20 and that adds one of your skill modifiers.
Stat checks, attack rolls, saving throws, and any other 1d20-type checks still work as normal.
An exception to this is the Use Magic Device skill; because special things can happen on extreme rolls for that skill, it still uses 1d20 instead of 3d6.