Go to the Project you're submitting the expense to and click "Submit Expense". You will need to upload a receipt or invoice and provide your contact details and PayPal address.
Each Project (and its Fiscal Host) can specify expense policies and helpful info like the details for invoicing, at the top of the 'new expense' page (example).
You can submit two kinds of expenses:
A receipt to be reimbursed for something you already paid for.
An invoice for your time or work, or if you don't have a receipt.
Here is an invoice template you can use. Fill out the blue parts, and change the payer to the correct Fiscal Host if needed (the Fiscal Host is shown under the Project name on their page, and this info should be in their expense policies, which appear on the 'submit expense' screen for the Project. If you are a Fiscal Host, read this to know what billing address you should ask your project to use).
In order to be paid, submitted expenses must be approved by the Project's core contributors (admins), who ensure valid use of the Project's funds.
A valid invoice must include:
The word/title invoice
A unique invoice number and an invoice date (when invoice was generated)
Your full name and physical address
The name of the Project
The name of the Fiscal Host organization (for most open source software projects that's "Open Source Project")
Summary/description of what is for (working hours, services ..)
Total amount payable
Payment details (how to pay you: bank details, PayPal, ...)
Private information provided on invoices is not viewable publicly. The expense amount will be listed on the Project's public page, but the invoice itself is only visible to the host and core contributors.
A valid receipt contains:
Name of vendor (person or company you paid)
Transaction date (when you paid)
Detailed description of goods or services purchased (what you bought)
Form of payment (cash, check, or last four digits of credit card)