Here are the steps I took to deep clean my coffeemaker. Now, keep in mind that the total, overall length of time to do this will be 10 minutes, but it will only take about 10 minutes of your time to actually set it up for the cleaning.
#1 - Empty/clean out the filter basket and coffeepot.
#2 - Fill your coffeepot with 1 part white vinegar, 2 parts water and pour it into the coffeemaker. Put a new paper filter into the filter basket to catch all of the loosened junk.
#3 - Brew the water and let the coffeemaker run through the full brewing cycle.
#4 - When the cycle finishes, unplug the coffeemaker and let it sit to cool down (about 15 minutes).
#5 - Dump out the water/vinegar mixture from the coffeepot. Throw away the paper filter.
#6 - If the inside of your coffeemaker has brown coffee stains all over, now would be a good time to clean these (if you want). The water vapor inside the machine has vinegar in it, making it a good cleaning solution for the stains. I used a Q-tip to clean the hard to reach places, dipping the Q-tip in the hot water/vinegar mixture that was in the coffeepot.
#7 - Repeat the cycle with water only two more times to clean out any vinegar that was left behind. You may continue to see more crud come out into your filter, so you can put in a new one if you want. I don't use paper filters, so I only have the 3 that came with the machine. I didn't want to waste it, so I just cleaned out the filter basket after the two water-only cycles.
#8 - Run your coffeepot and filter basket(s) through the dishwasher.
Okay...so it may take you longer than 10 minutes...but it's worth it. =]