Welcome to ProZ.com!
What I would suggest on a general note is to go through the relevant forums here: besides Money Matters, you should find a vault of information in Getting Established, Being Independent and Business Issues.
Regarding your specific issues:
Just wondering, what is the course of action, for acceping translation jobs. Let's say I get in touch with the client through e-mail, and they send me the necessary files. Do I have to send them an invoice after?
Definitely yes, as your client will need to account for the payment.
and if so, how do I make the invoice??
Search the forums for "invoice", and check with your tax adviser (or local tax office) what the required elements are in your jurisdiction.
Also, first job I ever took was a small one around 800 words. It was a PDF file that I had to translate to word. They were happe with it, even asked me how I was able to transfer the images, and I gladly told them. They haven't replied since though. Now all I have is an email of theirs. Maybe I should have asked what their company name is? and their physical address first?
You should get a purchase order ("PO") containing the outsourcer's contact details, job details and payment terms.
What other steps should I have taken to prevent something like that from happenning again?
Maybe they're simply waiting for your invoice...? Have you called them?
I still have their file, it was legal documents for a patent translation. So there is alot of info in that. Maybe I could track them somehow through that?
Sure, why not?