Has the order been approved? Look on the Billing > Overview page. Do you see an "Orders" widget? If not, click Manage Widgets and drag it from the right to the left. That will put the widget on the Billing Overview page. Has the order been approved? If not, it must be approved first. Only paid pending services are provisioned, so the invoice must also be paid.
If those conditions are met, your cron will try to provision the service within 5 minutes. Is your cron active and working? Check Settings > System > Automation, does it have a recent last run date? You can try running it manually here if your cron is not working properly.
If the service is listed as a pending service, and the cron has run, there may be an issue. Check the module logs as Mike mentioned under Tools > Logs > Module, click the row to expand and display the raw input/output.