While technically playing a roleplaying game requires nothing more than a copy of the rules, a set of dice, and some scrap paper, every gamer knows that there's an awful lot of information flying around the game table that needs keeping track. Back in the long ago days as a teen-aged DM for my younger siblings and cousins, we had some fixtures on our game table that accomplished a lot of that pretty handily.
To keep track of combat, we used a sheet of paper with a grid drawn with ruler and marker, under a piece of 1/4" thick glass about 14 inches square. I think it was a grid of half-inch squares, but I can't recall for certain. For a long time, the whole thing was physically attached to the center of the table with carefully applied duct tape. We'd use a wet-erase marker to draw the walls and other features of each theater of battle. For the combatants themselves, we had a jar of buttons. On a bunch of the plainer ones, I had painted numbers with model paint; these were the monsters. Players usually chose from among the cooler and more ornate buttons for their PC tokens.
Nowadays we use miniatures, but I miss the button system and would like to get back to it. Why? Because with numbered buttons, it's easy to keep track of separate hit points for multiple monsters. Because buttons don't tend to fall over if the table is jarred or somebody's hand twitches while moving a figure in a crowd. Miniatures are cool and all, but I'm all about function over style. Hopefully my current group of players will concur...
We also had a paper-and-glass character stat tracker, which was taped to the table at the DM's spot. It had lines for about eight characters, and columns for listing Armor Class, hit points, and Notes. The hit point space was amply large to accommodate adjustments due to wounds and healing. Often I'd record the maximum hp in a different color. The Notes column was used for such things as who was holding the light source or wielding the maybe-magical weapon the party discovered earlier. There was plenty of room at the bottom margin to keep track of a small army of monster hit points during battles.
I heartily recommend wet-erase markers over dry-erase for the simple reason that things aren't going to be inadvertently smudged or erased when you lean on the table to reach something or deliver a dramatic oration. The spray bottle of water and heavily blue-stained rags that we kept at the table became almost as symbolic of the game to us as the dice.
There was an extra slab of glass or two, which I'd sometimes lay atop the map of the adventure du jour, so I could mark the party's position and progress without marring the map itself with scratching and erasing. This was about the only use I had for a screen at the table. I didn't sit behind the screen myself, but had it to one side, protecting the all-important map from prying eyes.
There are a few things about the old days that I don't miss much, too. Back then, we didn't have access to a computer and printer, so actual character sheets were a semi-precious commodity. New characters were scribbled on notebook paper, and generally didn't get a character sheet until 2nd level, when it had proven its ability to survive both the rigors of the dungeon and the fickle interest of the player.
For a long time we had only one set of dice, and they were the butt-ugly dull plastic ones that came with the Moldvay Basic Set. We used the hell out of 'em, though. When we finally acquired the Mentzer Expert Set (I think Moldvay/Cook was technically already out of print, ours being a second-hand copy), we upgraded to the much higher-quality dice that came with that set. We shared the dice between DM and all the players, and despite never having any issue with it other than the delay when someone sent a die clattering off the table, I like having several sets of dice on the table. They're still mostly communal dice, except for my nieces, who got their own sets for Christmas last year.