Since .NET 4.0 there is no need for this hack with IHttpHandler to load Session state (like one in most upvoted answer). There is a method HttpContext.SetSessionStateBehavior to define needed session behaviour.
If Session is needed on all requests set runAllManagedModulesForAllRequests to true in web.config HttpModule declaration, but be aware that there is a significant performance cost running all modules for all requests, so be sure to use preCondition="managedHandler" if you don't need Session for all requests.
For future readers here is a complete example:
web.config declaration - invoking HttpModule for all requests:
<system.webServer>
    <modules runAllManagedModulesForAllRequests="true">
        <add name="ModuleWithSessionAccess" type="HttpModuleWithSessionAccess.ModuleWithSessionAccess, HttpModuleWithSessionAccess"/>
    </modules>
</system.webServer>
web.config declaration - invoking HttpModule only for managed requests:
<system.webServer>
    <modules>
        <add name="ModuleWithSessionAccess" type="HttpModuleWithSessionAccess.ModuleWithSessionAccess, HttpModuleWithSessionAccess" preCondition="managedHandler"/>
    </modules>
</system.webServer>
IHttpModule implementation:
namespace HttpModuleWithSessionAccess
{
    public class ModuleWithSessionAccess : IHttpModule
    {
        public void Init(HttpApplication context)
        {
            context.BeginRequest += Context_BeginRequest;
            context.PreRequestHandlerExecute += Context_PreRequestHandlerExecute;
        }
        private void Context_BeginRequest(object sender, EventArgs e)
        {
            var app = (HttpApplication)sender;
            app.Context.SetSessionStateBehavior(System.Web.SessionState.SessionStateBehavior.Required);
        }
    
        private void Context_PreRequestHandlerExecute(object sender, EventArgs e)
        {
            var app = (HttpApplication)sender;
            if (app.Context.Session != null)
            {
                app.Context.Session["Random"] = $"Random value: {new Random().Next()}";
            }
        }
        public void Dispose()
        {
        }
    }
}