First; there's some info required to try to troubleshoot... What are your system specs (CPU, RAM, Video card, etc.)
Are you getting any errors in the console or logs? And there are ways to get extra logs... which I'll go into shortly.
Second; having said that... now I'll ignore myself and try troubleshooting blindly. Because that's the sort of Computer guy I am.
There is an issue I and some others have had where (depending on system specs) the game requires more RAM for Java than the Java defaults will allow; so you end up with a Java "OutOfMemory" error that crashes the game. I'll pretend that's what you're seeing.
Which is sad, and disappointing; and if you're ok running the game outside of Steam... totally fixable. You'll end up running a lightly modified batch file from a batch file they provided (so it's pretty normal).
Now my system is integrated video, dual core, with 8Gb of RAM... so I had a lot of ram to play with and decide to allow the game 4Gb. If you've only got say 4GB you might shutter at 2048 instead of 4096 in the change at the link provided.
I tend run actually run at 1.3-1.4Gb of memory used for the ProjectZomboid process with this batch file; but I don't get hardly any lag; and my crashing issues stopped.
IF this doesn't help (and it very well may not help) it WILL give you more info to provide. you'll get an error logfile (I called it err64.txt, you can change that in the bat file) which dumps into the Steam Project Zomboid folder... and with a logfile it's a lot more likely you'll get more detailed and specific help.
