It's a bummer but your mountain bike needs care, love and attention (just like the family cat).
It's strangely cathartic to return your abused bike to show room condition. Apart from the aesthetics, the cleaning process lets you assess the condition of your bike's components so you can catch potential problems early (a stitch in time and all that...) A dry rag works best. If it's really grotty then a preliminary gentle wash helps but remember that bikes hate water (just like your cat). Don't squirt with high pressure - the water works it's way into hubs, pedals, shocks and bottom brackets to cause permanent rust damage.
Regularly cleaning and lubing your bike's chain reduces wear and improves shifting performance. Worn chains are bad Karma. They drastically increase front and rear cog wear. With replacement drive trains setting you back $150 plus, looking after the business end of your bike is well worth the effort. (Some modern lubes like Rock 'n' Roll are self cleaning, minimising the need for all this additional maintenance. Worth a trial unless you ride in very wet and muddy conditions.)
With time, cables stretch causing imprecise shifting - typically you'll find it difficult to select the biggest cog or the rear derailleur makes ghastly clicking noises when you attempt to change to an easier gear. It's simple to tighten cables by screwing the barrel adjuster by the gear shifter anti-clockwise. If that doesn't work, let your shop mechanic loose on the problem. Cables also enjoy being cleaned and lubricated - which helps to ensure featherlight shifting. Here's the trick - select the largest cog at front and at the rear (while pedalling) then relax the shifters while stationary, ie. select 1 at the front and 9 or 10 at the rear. The cable goes super slack, allowing you to remove it from the lugs on your frame. Slide the casing to one end - exposing the cable at the other so you can clean it - use CRC on a dry rag then a small amount of light oil or dry lube. Then move the casing to the opposite end to do the remaining cable. Refit the cables and tighten the cable with the shifters.
Brake pads wear and need tweaking. Modern hydraulic systems generally self adjust. Replacing worn pads is normally quite straight forward. Beyond that you'll need to engage the services of your local bike mechanic.
Tighten the obvious with an Allen key or spanner - boogie down to your local shop for the uncertain. Components you should keep an eye on are: