I use my bicycle in a typical urban commute setting. No extreme MTB, but it still accumulates some dust and grime.
How should I wash my bicycle?
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Cycling Tips has some useful pointers.
On the urban commute you do not want to be constantly degreasing and lubing the drive chain. Simply keep it lightly oiled so that it is lubricated but not attracting dirt.
If you have normal rim brakes then you will collect that evil dirt on the wheels/rims from braking and this can be hard to shift with soapy water. What you need is washing powder, that stuff you put in the washing machine. Put a small quantity in a bucket of hot water and, with the clean water, give the frame a going over with a soft cloth or sponge.
Get a small screwdriver and clean what you can from in between the sprockets, jockey wheels and chainset. Pedalling backwards whilst holding the screwdriver in place should lift off most of the built-up debris.
Now give the components a quick once over, recommended tool being a brush in the hot washing-powder enhanced water. Use nothing too abrasive, the brush from a dustpan and brush will suffice and can be replaced/disposed affordably.
Now do the wheels. The washing powder should work wonders lifting off the evil black stuff. You can hopefully get in between the spokes and do the sides quickly if you spin the wheels round.
Now you can wash the bike with clean water. Cold is more eco-friendly. Have a look underneath to make sure you have not missed too much. Bounce the bike a few times to get most of the water drops off and then give it a quick dry down with a cloth.
With an oily rag go over the hex bolts and other areas where you need a light coating of protection from rust. Put your favourite lube on the chain and spray minute quantities of 'GT85' on brake pivots, gear mechanisms and catch the excess with a cloth, making extra sure that none of it gets on the rims.