How does one fire from a bow again. Is it a case of having the bow as primary and the arrows as secondary. What's the range on them?
wield your bow as primary weapon, and quiver your stack of arrows. Then use f to fire. Moving into an enemies in that state would mean you smack them with your bow. You can press x to switch to your secondary weapon slot, and w a melee weapon there. Then you can x between the two easily.
Range is random, but adjusted according to your strength. Try a few times and make a note. Test again if your strength changes.
Z to cast spells. You will be presented a list of spells you know. Be careful... your character will eventually (after a large amount of turns) forget how to cast the spells. Those spells will be marked with an asterisk, and trying to cast them would confuse your character as your magical energy goes wild.How does one use spells?
Does anyone have a complete listing of the controlls?
It's in the guide (Guidebook.html) that comes with the game. You can also press ? in the game to display the in-game help.
I keep getting so far (usually the mines) I tend to pick up alot of stuff but never seem to get anywhere.
Exploration is a big part of NetHack, to figure out how you can use an item you've found. Many items have a number of different uses... I'll let you have the fun of exploration.

Just one advice: Don't pickup too much. If you get burdened (or the other more serious levels), you will only able to act once every few turns. Your enemies in the mean time can hit you freely. Drop items you don't need... setup a stash, take note of where it is, and return to it later if you need something.
Setting up a stash so other intelligent inhabitants of the dungeon cannot pickup your things though, is another important lesson you'll have to learn...

What are the gems and the like for? I tend to accumulate a few
You can sell them in shops (by using the drop command)... not all types of shops buy gems though. If it said the shopkeep is not interested, you can pick your gems backup and try another shop.
Also many gems are made of hard materials... you can throw them if you run out of projectiles. Using a sling to throw gems will get you better range and damage.

There are also rumors that unicorns love gems... unicorns come in three colours, black, white and grey, which is interestingly related to your character's alignment, chaotic, lawful and neutral...
