Currently the game doesn't support switching out custom maps using the UI, so a tiny bit of playing around with folders and files is required. Basically, the way it works is that the game will load whichever map is named test.tmx. Obviously having a load of files called test.tmx in the same folder is not going to work, but there are ways to install a bunch of user created maps with minimal file-juggling.
First off, download whichever custom maps you're looking to play. Extract them to a folder outside of the Project Zomboid directory (anywhere will do). Often they'll be uploaded with the filename test.tmx, so after each download, rename the file to something else, either numbering them or giving them a keyword based on the map description (example: hospital.tmx for the hospital map). Eventually, when you've grabbed all the maps you're after, you'll end up with a folder of .tmx files. Now go into the Project Zomboid Media folder (C:\installdirectory\Media on PC, Contents\Resources\Java\Media on Mac) and find the file test.tmx. Rename this to whatever you want – default.tmx, perhaps. For safety, copy this over to the external map folder you created earlier so you have a backup.
Now copy all the .tmx files in your external map folder over to the Project Zomboid Media folder. You now have all the maps ready in your PZ folder. Rename whichever map you want to play, as test.tmx then when you're done with it and want to play another, change its name back to the defining label you've given it, and change another to test.tmx. Keeping them all in one folder and simply renaming them is easier - and hopefully less confusing - than switching files in and out of folders every time you want to play one of the maps you've already downloaded.
All set? Good. To begin with, our forum-dwelling modding genius Ringod123 has cleverly incorporated a large amount of individual map add-ons into one large, double-sized map comprising of, on one side, the original vanilla map with an added maze from VindalooJim, and on the other a whole host of community-brewed creations. It comes complete with a vast array of unique buildings and features, all available for individual download on the forums, so for a detailed list and download head here. To see this map in action, take a look at Ringod's videos where he continues to demo a range of different mods, including this map and various sprites too.
On equal footing with the epic size and scale of Ringod's mod mash-up is another map, originally built by forumite Andrew for 0.1.4 and updated to work in 0.1.5 by Ominus. The map, again, features multiple smaller map mods made by others in the past and put together. There's all sorts; a bar, café, police station, motel, church and more, all available here.
On the other hand, a complete conversion of the default map comes in the form of Triptych's Cloquet. Set in an apocalypse where survivors have been forced to retreat back to caves on the other side of the river, the map features a fully kitted-out, homely cave labyrinth, bridges to cross the river and the town where the zombie horde roams tirelessly. The map brings a welcome freshness to PZ for those who have played the vanilla map to death. Pun intended. You can take your chances in the caves by downloading Cloquet here.
If you're sick of the shopping district in PZ's standard map, you can also download Mendonca's hospital which removes the map's western buildings in favour of this medical maze. The mod boasts hundreds of rooms as life threatening as they can be life saving. Zombies wander in its distant halls and fester in its yards. The windows are bare and leave you vulnerable unless you can fortify a safety nest within, though a treacherous walk to the kitchen can have you straying far from your haven.
There's a huge number of PZ map mods, big, small, some quirky and some thoroughly designed. The community's scope is only as limited as their tools, and as such we plan to introduce more modding capabilities at a later date. For now, though, a thoroughly long list of downloadable mods and tutorials on how to build them can be found by visiting our forums.