In a wordpress multisite, an user can create as many blog as he wants. If you Pro Sites you can control this. Pro Sites is a giant plugin that will help you to have control over the whole network.
But if you just want to limit one blog per user in a wordpress multisite and donâ€™t want to use a huge plugin like Pro Sites, then this small snippet should help you.
You can add those codes in your functions.php in the theme, if you think your theme wonâ€™t be changed. Otherwise mu-plugins is the best solution. To use mu-plugins, go to /wp-content/ and find the folder with name â€˜mu-pluginsâ€™. If there is no folder in that name, then create a folder, name it â€˜mu-pluginsâ€™, create a file inside that, give any name you like and paste the code in there. You donâ€™t need to activate that plugin. Mu-plugins means must use plugins, so it will be activated automatically always. If you use mu-plugins then add a php start tag at the beginning of the code.