Here are the tools I use regularly, so I always include them on either my Props table or on the display table. Each of these should be explained as necessary.  Decide which can be used as hands-on items and place all sharp or dangerous tools to the back of the table, away from children.
 

Bee smoker and bellows

Nothing is more important than a quality smoker. Choosing one is simple. Buy a good stainless steel smoker with enough capacity ( internal space for burning material ) so that you don't have to reload during any given inspection. Do not skimp here, your smoker is the difference between a fun inspection and a frenzy of grumpy bees. I keep a cup of sand handy to pour into the smoker after each use - this kills off any flames that remain and eliminate the chance of starting a fire. Clean after each use and store in a dry place. 

Clean Burlap

This is the fuel for the smoker. There are products on the market today that is safer, longer burning and easier to light. I still use burlap and I find it a good fuel which produces a good quality, low temperature smoke. Be sure that it is clean, free of any oils, greases, paint or other hazardous chemical that will kill the bees. I wash my burlap sacks and air dry them. I cut them into roughly one foot squares, then store them away in a sealable plastic bag. One or two of these squares will give you about 20 minutes of smoke. Always have a handful with you at the hives and loosely pack a few into the smoker when ready to begin inspection.

Barbecue Lighter

I like those long lighters used for lighting barbecues to start the burlap in my smoker. It keeps my fingers away from the fire and and allows me to pump away at the bellows. You can of course use a regular cigarette lighter or matches, but for a few bucks, you'll have this stowed away in your smoker.

Leather gloves

Good fitting, long sleeve, vented gloves are a pleasure to use when working with the frames. Don't think that beekeeping ISN'T messy, cause at times it gets down right sticky and dirty. Leather gloves are sting proof and very flexible when properly fitted. They will last for years if properly cared for. You need to clean and wipe the gloves after every use. I wear the gloves and wash my hands under warm water, dry them immediately and then rub them down with olive oil and again remove as much excess oil as possible. Finally, I store them flat in my cabinet.

Hood and Veil

When it's time to get down and dirty, you will need a hood and veil. I use a square faced hood that keeps my face plenty far from the screen on all sides. There are many types of hoods to choose from, this is one piece of equipment that you can pick out without any coaching from me. Just find one that you really like and take good care of it.

Goggles

If you don't wear a hood and veil, then I recommend you use goggles or swimming glasses to keep the bees from accidentally flying into your eyes. I've been stung thousands of times and never been stung in my eyes, but I sure wouldn't look forward to it. An ounce of prevention here will give you a great amount of piece of mind.

Hive tool

This is a simple pry bar like tool with a notch on one end for pulling nails and scraping cappings. Also, it has a bent lip on the opposite end for prying frames and boxes apart. I've used many different objects, knives, small crowbar, hatchet and almost anything I could get my hands on. But the hive tool is really ideal. It's light, tensiled and perfect for handling with leather gloves on.

Frame grabber 

A handy too is the frame grabber. It is a spring loaded tool that allows you to grab a single frame with just one hand. It does take a bit of hand strength to hold on for long periods of time, but with just a twist of the wrist, you can see either side of the frame. I like to use the frame grabber for pulling the frames out of the super and for holding them securely as I scrape cappings or remove excess wax.

Empty deep box shell

I keep several empty supers handy for several reasons. I often pull several frames out of a hive during inspection and I need a place to put them. The empty super also makes a good stand to place other supers on, thus keeping them off of the ground.

Magnifying glass

I keep a quality magnifying glass handy for many reasons. I like to look closely at the bees, inspecting for mites, checking the cells and looking closely at the larva and eggs. Note: be careful not to fry your bees if the sun is above or behind you. Loosing a worker is not a big deal, but cooking your queen is a great way to slow down your hive growth really quick. Also, the bees are not as keen on the idea of the magnifying glass as we are. Often, the will get active as light patterns pass over them and as the look through the glass.

Log Book

As with any job, there is paperwork. You will be glad that you started a log book after several months of beekeeping. I have kept one since my earliest days in the hobby. Nothing special is needed, just a simple book with enough room for a few seasons of notes. I keep the following information in my book.
 

• Date inspected
• Number of colonies
• Number of swarms spotted
• General health
• Any signs of disease
• Whether I spotted the queen or freshly laid eggs or young larva
• Anything note worthy or different from last inspection