I have a sliver protection color and my oponent use fog and my protection is from green my question is the fog afect my protection or how works the protection
The easy way to remember how protection works is DEBT
D - damage from sources of that color is prevented
E - enchant/equip Creatures cannot be equipped or "enchanted" by permanents of that color. If an equipped creature gains protection from artifacts, the equipment will stop being attached to that creature. An aura of that color would "fall off" (be put in the graveyard.)
B - blocking Creatures with protection from a color cannot be blocked by other creatures of that color.
T - targeting anything with protection from something can't be targeted by those things. For example {Progenitus} cannot be targeted by {Go for the Throat}. Remember, the word "target" must be there for protection to work.
Anything else is not affected by protection. {Day of Judgment} will destroy a creature with protection from white. So to answer your question, the {Fog} will prevent the damage from a pro-green creature.
Since this post is all about protection, I figured I'd throw in a few things I've learned:
Trample can get over a creature with a relevant prot. After assigning lethal damage (which is then prevented), the rest goes at the players life total.
Abilities like deathtouch and lifelink will not trigger against prot, since no damage was done. Same with any abilities that trigger on damage (eg. {Curiosity} )
If you happen to have deathtouch and trample, you only have to assign 1 point of damage on the blocking creature (since that'd be lethal), then the rest goes to the face.