So you've successfully created a player run plot and then submitted it. The plot was deemed fine and peachy, and now it's time to run it. How should you go about doing this?
First, know and love the public plot grid. Each plot room has one associated with it, and anyone in that room can use it as they wish. The plot grids are specialized spreadsheet widgets that allow random people to write things on them. Anything written or changed on one will be visible to everyone else looking at that page, provided they have a Java-capable browser. Plot grids also have small square icons that can be click-dragged around on the grid, showing exact relationships between PCs and enemies. On the right-hand side of the grid, you can note down PC and monster names, initiatives, current hit points, and spells in effect, while on the left-hand side you can plot out any combat that goes on.
It can often be convenient to represent buildings or terrain on the grid. To do so, click-drag to select an area of the grid, go to the Format dropdown menu, select Background Color, and choose something appropriate. To make square buildings rapidly, it's easiest to create a large block on the map, and then "hollow out" the interior with a block of no-color. A single block on the edge can then be turned into a door, and poof- it's a square room or building. The same technique can be used to create a dungeon map, blacking out a large chunk of the grid and erasing holes for corridors and rooms as PCs discover them. Similar tricks can be used to reproduce outdoor areas with important physical features.
Second, choose your plot participants. For new DMs, it's best to have no more than four PCs in the party. More than that, and it can be tough to keep track of them and the monsters both. Even at its largest, a plot probably shouldn't have more than six people. Two or three-person plots are entirely fine, and can often move much faster than larger ones. Making an announcement over the PrP Channel is wise. Players are automatically added to it, so you should be able to broadcast your invitation to the whole MUX by just using "prp I'm running a plot now. Who wants in?".
Third, get an unoccupied plot room, use "+setdm" to gain DM powers there, and run it. It's often important to make clear any special rules or expectations you might have beforehand, so there's no confusion. It's generally best to make clear that you're not using any sort of "pose order", and that nobody should wait around for everyone else to pose if they've got something they want to say or do. If every member of a four-person group took four minutes to make a pose and all of them waited their turn to do so, they'd get about four poses apiece per hour- and that just won't work for a plot. Players should be encouraged to pose briskly and without undue tardiness. Players who idle at inopportune moments are perhaps best served by staying out of plots until they can give their whole attention to it.
Combat is a particularly sticky point. A lot of decisions have to be made, and a lot of communication has to take place between players and DM before the players can sensibly decide what to do. They have to know how many enemies there are, where they are, and where the PCs are in relation to them. Help them out by setting up the plot grid clearly, so PCs don't have to wonder if they can Charge orc #3- they can see it on the map. Encourage players to roll damage at the same time as they roll their to-hit roll; if they missed, you can ignore it, and if they hit, it spares them asking "Did I hit?" and waiting for you to answer yes or no. Get the PCs' armor class, spell and HP info before you start the plot, so you don't need to stop mid-fight and find out whether the bugbear's attack roll of 17 hits the fighter.
In a fairly large group of 4 or 5 PCs, you might have time enough to let each of them pose after their actions each turn. By the time their turn comes up again, they may've had the few minutes needed to make a pose. Or you may choose to let them make poses at the end of the fight, giving a few "combat highlights" of their most impressive attacks or grievous injuries. However it's done, you should never be waiting for someone to pose. Combat takes a lot of dice rolls and a lot of time as it is- each minute spent waiting for the wizard to think of a new way to describe his fifth magic missile of the fight is a minute that everyone else has to wait to have fun. With only two PCs, you might have the luxury of allowing individual poses and waiting a bit, but once you get to four or more, there's just no time to sit around while the fighter looks up his 37th synonym for "cleave".
Spot and Listen checks are some of the more annoying checks to deal with. Every time the players are at risk of being surprised, everyone has to haul out a d20 and make a roll, which is then compared to the roll of whomever's Hiding or Moving Silently towards them. You may want to take a page from the upcoming 4th edition of D&D, and treat the PC Spot and Listen checks as static values. Just take their Spot and Listen scores, add 10, and that's the number that a Hide or Move Silently check has to beat in order to bushwhack them. Instead of having to wait for the whole party to make the roll, you can simply make the Hide or Move Silently roll yourself, and then compare it to their scores to see which of the PCs noticed.
Finally, be ready to make quick calls. PCs are always doing something unreasonable and unpredictable, and they expect you to tell them whether it works or not. It's handy to have www.d20srd.org open when you run a plot- you can easily click to see the specific detailed for Bull Rush or Improved Trip or the range on a specific spell. If no rule exists or you don't have time to look it up, just make a call that seems reasonable to you. It may or may not be absolutely correct, but as the DM, it's your game. Staff is not going to punish you for making a "wrong" call, even if it's contrary to the canonical rules. It's best to follow the given rules when possible, but if a player doesn't like your judgment, then he or she is under no obligation to go on your plots. There isn't always time to look up every fiddly detail, and a decent answer now is better than a perfect answer after five minutes of idling.
Once your plot's complete, you can make a note of its participants and the general outcome with the +myjob/add <job #>=<text> command, and can get a list of plots jobs you have with +myjobs. No logs, extensive notes, transcriptions, or other deep paperwork is needed- just a few sentences describing roughly what happened. You can also make suggestions for adding to the Recent Events entries on the wiki. Staff will then make the payout in XP and treasure for participants, and you'll have a number of players grateful for the good fun you've provided them.