No problem - we're all new at some stage! Are you using the Email Program, or just a Default Program?
There's no alert you'll receive when a campaign has been sent, and you could set up an alert yourself, but at first I would recommend checking the results in the Marketo interface so you're familiar with it all. Generally, we will first send out our emails to a static seed-list only (add as a filter in Smart List tab), as a final testing step. This list will contain leads that are actually members of your internal team. If all is well, you can then remove the static list filter from your Smart List, double check the leads #, then you're ready to go.
Once the campaign has been sent, you can check the Dashboard (if using Email Program) or Results tab (if using Default Program) to see the status of your campaign instantly.
Don't forget to test thoroughly and take small steps at a time. Hope that helps!