The most common (and inexpensive) way to clean your coffee maker’s insides: Pour equal parts water and white vinegar into your coffee maker’s water reservoir. Run it through one cycle (with no grounds obviously). Rinse and repeat on a monthly or bi-monthly basis.
Cleaning Your Coffee Pot: Disassemble and run it through your dish-washer. For cases similar to mine: Scrape the thick layer of mineral deposits off the inside then run it through the dishwasher.
And now, after years of secrecy I will reveal the highly efficient method I have developed for keeping my own coffee maker in tip-top shape:
I clean it when my wife tells me to. This usually occurs when she can’t stand to look at it anymore because (in her biased opinion) it looks gross. The main benefit of my secret coffee maker cleaning method is the opportunity it gives me to potentially never clean it. The efficiency of my secret method is undeniable.
Eventually (after a few years) my coffee maker will clog up with mineral deposits to the point that water can no longer cycle through. At this point I will throw the whole thing away and get another $10-20 Mr. Coffee machine on sale at my local grocery store. Low-maintenance household appliances FTW.