How can I run a game of D&D sporadically?

Take good notes and remember for the players.

1. Take good notes. Don't rely on your memory for what happened. Instead, take notes during the game and then allot about an hour for going over and adding to those notes. Basically what you want to have when you're done and packing away your notes is a little kit of information that will tell you everything you need to know to keep running the game. Expect to completely forget anything you don't write down, and that will make sure that you have useful notes. Treat it like you're preparing notes for another DM to pick up where you left off!

   Then, weeks or months later when it's time to prepare for the next session, you can take those notes out and read them as the “background” for the next adventure, as if you weren't even there.

2. Remember for the players. During the game, be your players' memories. When you bring in an NPC that they previously interacted with, make that part of their reintroduction. (E.g., “A tough-looking woman with a broadsword on her hip enters the tavern. She's Meredith, the mercenary that you worked with briefly but parted on poor terms with. She hasn't noticed you and walks over to the bar…”)

   By being generous with this information, you make up for what the players are missing: immediate recall of what just happened last session.

These two things are all you really need to make a session work after a long time. Provided you have players who want to be gaming (i.e., enthusiasm waning due to long breaks isn't an additional issue), these practical steps all that's necessary to patch the time gap.

Best way I've seen to run a game when you can't be sure when the next session will be -- is to plan for each adventure to take only one session. These can be parts of a longer term, coherent campaign (and it's more fun, in my experience, if they are), but there should be no need to "pick up where we left off" at the next sitting; that way, if a player can't make a session, you can carry on. Likewise, it simplifies introducing new characters if you don't have to find a way to retcon them into the group, and it doesn't require everyone maintain detailed memory of the exact state of things at the last session -- but characters can build up over time, just as they would in a more continuous campaign.

I strongly encourage my players to write a diary. In our last game the diary is written during the game by the player least involved or most enthusiastic about the diary. Before every session a player reads the entry for the last session.

I feel this is a good solution as it achieves several things. First if it reminds every one of what happened last time, and secondly the reading of the diary aloud acts as a transition from goofing around and socialising to starting the game.

Also the diary is a good place for the DM to look to understand what the players are interested in and what clues they are picking up on.

I would caution against the DM writing the diary/log because the DM's perception of what happened and how to interpreted it my differ significantly from the players perception. Worst case the DM ends up revealing new plot information.

This is going to sound very old school but it is the best way to handle games that have long periods between sessions or where some players are in and out a lot and it is hard to know what the party composition will be. Play a traditional mega-dungeon or dungeon crawl style of game.

The advantages to this strategy are numerous.

First, prep is easy for you as the GM. It's a site based adventure where you have fleshed out the places they are likely / planning to go. You aren't having to try to track lots of story plotlines and such and a quick glance over your notes and the module itself will get you ready for the next session whenever it is.

Second, each session can be a delve into the dungeon and then returning to the base village / town. Longer sessions can have longer delves while shorter session concentrate on exploring a smaller area. This makes each session very episodic, much like a single episode of Stargate SG-1.

Third, because each session is a single delve into the dungeon, players can come and go between sessions. It no longer matters at that point which / how many players show up for a specific session. That session's delve can be determined based on who showed up.

There are some things you need to be careful about in this style of play. The biggest one in my opinion is the tendency for it to become a "Kick in the door and kill the orc and take the loot." style game. It doesn't have to be that. Look at whatever dungeon you are using; Keep on the Borderlands, Temple of Elemental Evil, Rappan Athuk, whatever. Pick out the most interesting villains, NPCs and places. Seed them or rumors of them early in the game. A little bit of effort will make the very episodic style of play still have some threads that make it seem like a more coherent storyline. I mentioned it earlier in this thread but watching Stargate: SG-1 is a good way to get some ideas on how to run this style of game. It is essentially D&D with Sci-Fi trappings.

Hope that helps some.

I'm going to extend upon some other answers that I have seen with some additional points since this is something I have done frequently.

1. Track everything. Keep an up-to-date log of all the encounters, interactions, etc for the party. This makes giving a recap every easy. I personally like to make note of the funny/interesting things as well (easier for people to remember the barbarian hurling a log downstairs and crushing the face of a pursuer - rather then the fight against 5 CR 3 bandits).

2. Plan when you remember the setting, not after. I always plan out the next couple of sessions ahead. When I know there will be a longer then normal break (more then a month) I will plan most of the campaign. This helps with that feeling of being connected.

3. Keep a copy of everyone's character sheet. Far too often do you go to start a campaign again only to have party members forget/lose their character sheets.

4. Get a lot done in every session. It keeps things interesting for the players, and makes the single session much more important. Follow good DM practices for keeping the campaign moving at a good pace.

Most of all, have fun!

Also, this may not be well received - but I personally use google documents for my campaigns. It means I can DM from anywhere with an internet connection. Also if it is an online campaign, you can share certain sheets with characters (especially useful for maps, PDF's for rule books, etc).

It seems to me that your biggest issue is story immersion of your players. Normally, I'd ask one of the players to make notes, another to keep track of money and treasure and another to keep track of NPC encounters. However, you have a party filled with new RPG players so you're going to have to do the note taking. At the beginning of each new session, take 15-20 minutes to recap what's been done (to help with story immersion, talk in second person and look at the player whose character did the stuff). Hopefully, your gaming sessions last more than a couple of hours at a time or maybe you could reduce the gaming session to a couple of hours and meet more frequently.

In our case the players keep logs themselves and the DM has a website on which he posts all the info of our campain: Our campain website

It keep tracks of the known legends, informatio about the towns and fellow adventurers thats commonly known and the journey so far.

Of course, you need to have the time to keep track and enter the information.