My opponent attacks me with say, a 6/6 trample generic Wyrm of some sort, and I block with a Whispering Specter, a 1/1 infect with flying. When damage is dealt the Specter will deal it in the form of a -1/-1 counter from its infect ability. Well, the Wyrm would normally deal me 5 leftover trample damage, so is this damage lowered by -1 from the counter given by the Specter?
No, you would suffer up to 5 damage if the opponent choose to assign the trample damage to you.
When two creatures deal combat to each other, it's simultaneous. So, for example, a non-trampling 6/6 would deal 6 damage to your 1/1, causing 6 damage to become "marked" on it, while, concurrently, your 1/1 would deal 1 point of infect damage to the 6/6, causing a -1/-1 counter to be put on it. The counters are the damage.
Trample doesn't add an extra step to damage resolution, it just changes how damage is assigned. So, a trampling 6/6 allows its controller to assign 1 damage to your 1/1 (since that's enough to kill it) and as much of the remaining damage as he wants to you. You, your blocker, and the attacking creature all take damage simultaneously.
If you blocked the 6/6 trampler with a 1/1 creature that had both infect and first strike, then its infect damage would be applied first, giving the 6/6 a -1/-1 counter, and then you'd only take a maximum of 4 trample damage.