Sharepoint 2013 - Create a site from a custom site-template using client object model

Here, is the code to create a site from a custom site-template using CSOM.

function CreateSite() {

        //load site

   var currentcontext = new SP.ClientContext.get_current();

   var currentweb = currentcontext.get_web();

   //site object

   var webCreateInfo = new SP.WebCreationInformation();

   //set values

   webCreateInfo.set_description("This site is created from CSOM");

   webCreateInfo.set_language(1033);

   webCreateInfo.set_title("My Title");

   webCreateInfo.set_url("/myURL");

   webCreateInfo.set_useSamePermissionsAsParentSite(true);

   webCreateInfo.set_webTemplate("MyTemplateID");

   //add sub site

   this.NewWebsite = this.currentweb.get_webs().add(webCreateInfo);

   //Load and execute query

   currentcontext.load(this.NewWebsite, 'ServerRelativeUrl', 'Created');

   currentcontext.executeQueryAsync(Function.createDelegate(this, this.Success), Function.createDelegate(this, this.oncListQueryFailed));    

}

function Success() {

alert(this.NewWebsite.get_serverRelativeUrl());

}

function oncListQueryFailed(sender, args) {

    alert('Request failed. ' + args.get_message() + '\n' + args.get_stackTrace());

}

Template ID is the most important thing here.It defines what is the type of site we are creating like would it be a Team Site,Blank Site, Wiki, Blog etc.
We can find all default template ID from here 
https://www.nothingbutsharepoint.com/sites/devwiki/sp2010dev/pages/site%20templates%20in%20sharepoint%202010.aspx

But , since here we are using our own custom site template . So we can get our template id from the code given in this blog.

Get web-template

Your custom site template id would  be in this format.
{GUID}#TemplateName