I'm currently creating some maps (dungeon, city) for a new 5e adventure I'm going to DM in a few weeks, and I stumbled upon a slight problem with player maps; Am I supposed to give them a map of the area with everything already drawn or am I supposed to draw the map dynamically when they explore the area? I'd guess that I'm supposed to draw it while they explore but seeing as one of my dungeons is currently drawn on an A3 sheet it would be a hassle to draw everything again, even with tiles as guidelines.
It depends on how much the characters can see, how surprising the details they can't see are, and how much you trust your players to not act in-character on out-of-character information. If you want to keep surprises from them, re-drawing the map as the characters move (as you suggested) is the classic way of dealing with this. But there are other options.
You could also lay out your existing map with areas covered by strategically-placed index cards or sticky notes. This is a nice, low-fi solution and usually works well as long as there isn't a breeze.
There is also the option of scanning the map into your computer and print out individual areas. This has the advantage of being able to cope with events that will happen to change the map after the characters have already seen the area, such as rock slides and cave-ins. You could also do this with an online program such as roll20.
Finally, a time-honored tradition is to describe the area and have a player draw the map as they go. This has the advantage of keeping the players involved during exposition, and giving them a bit of agency over their adventure.
For dungeons, I used to photocopy the map and cut out each of the rooms. When the players entered a new room I'd hand them that piece and they would put the dungeon together like a puzzle. Doing it this way takes a little more prep (<30 min), but it saves time at the table and some players will get really excited about collecting all the pieces.
I like this method for dungeons because it does a good job at hinting of where secret rooms might be based on the layout, without explicitly telling them. I don't think that it's a good fit for cities or countryside though.
Character knowledge and maps
I suggest to present maps in different ways depending on the characters' knowlege and how easy it would be to move in the area.
- If you have a city based adventure presenting an overview map including the diffent areas of the city allows the players to see that their characters could easily find out traveling through the city. As the action zooms in and focuses on a chase through backalleys I would switch to just describing the alleys - allowing players with knolwedge of the city to check for shortcuts and hidden escape routes.
- If later in the story an attack happens on characters homeground you can present a map. The characters know the layout. But you should hide enemies in fog of war as the characters have to detect those intruders by searching or listening etc.
- If the characters explore a dungeon or a unknown structure I suggest to show parts of the map as the characters move. So the players do not metagame your map and can feel clever if they can guess that some ways could lead to already know territories.
Exploring and showing parts of maps
There are some ways to give players such informations bit for bit.
- You can sketch new discovered parts to the players as the move on. I like this approach if your maps includes very long natural caves that you do not want to map out. You just sketch the interessting parts of the dungeon. Make sure to not only map out places with prepared enemies/encounters but also landmarks (the big fungi garden, the cave with a watersource, etc.). No your players can navigate that map with missing parts by telling you the landmarks. Your map is a graph and each vertice represents a special place and the edges represent passages between connected places.
- You can prepare a full map and uncover parts which have been visited. To represent a living environment you should allow monsters to move through other ways into the already discovered parts hidden by fog of war if the characters focus at other parts. You can cover the complete map with pieces that get removed or you cut your map in tiles rebuiding the map. For dungeon environments you can use dungeon tiles or even minature dungeon terrain. There are of course many electronical mapping tools that allow to use the fog of war feature.
- You can go the OSR way of just describing the dungeon and a player -- the mapper -- has to use this înformation to get a working map. This approach can be usefull if you have a interessting map including turning rooms, teleportation that will prevent characters from getting a working map easily. If you takes this route be sure that your players want to be challenged this way as getting a working map requires player skills and patience. Just to make carthograph skills helpfull you could use a Torchbearer RPG solution: if the characters have time allow a skill check and if successful give them a working copy of the parts already mapped or correct errors that the mapper made.
I suggest to work with every methode as it fits best parts of the adventure. And if you do not want to railroad your players you sometimes need to sketch a map as they just had this idea you could not think of while preparing for you session...
Unless there are hidden surprises, handing out a map or drawing on the spot is pretty much going to be your preference as a GM. I have no problem showing a map of the world/landmass (which would mostly common knowledge), or a city as even newcomers to a city can get a general layout from a local.
However, for a dungeon, I would take the time and draw it out as you go. In this case, the area is going to be more of an "unknown", and especially if you have cave-ins, secret doors, etc., it's hard to hide those if there is an entire wing that magically has no door.
If you want to provide a map and still cross them up a bit, you could give them an "ancient" map, and disguise/move certain things around, such as a cave-in/collapse that blocks off route A, but the local inhabitants have carved a passage leading from point D, etc.
I've written an application that may apply to your question. You would draw your map (or use a pregenerated map as from Rise of Tiamat, etc.), scan it, and then you can use the application to slowly reveal parts of the map to players. You can find the application and instructions here: https://github.com/apclary/dungeon-revealer This gives you the benefits of both approaches.