They just need an invoice for their processing and records. Just find a template online somewhere and use that. It just needs to say how much is owed, for what services, and who to pay the money to.
so on my end here in the US, even though i never did anything contractor wise or self employed, i dont need to register myself with any central entity or government entity to be able to issue invoices?
For example in my country, Portugal, where the actual company I serviced for is based at, if I were living there, I would need to register with the IRS in order to be able to invoice someone else and needed to give out my Fiscal number and so forth.
So in this case in the US, I just invoice them normally (with a template or create my own), all the details of services provided and payment options, and then receive the money ... do i need to make special arrangements with the money - like paying medicare tax or social security tax? or is that calculated at year end with my yearly income?