How does an umbrella company work in practice?

Here are the steps you will take if you join a UK-based PAYE umbrella firm:

Once you have secured a contract role, the umbrella company (as your ’employer’) signs a contract with your recruitment agency.
You will also sign a contract of employment with the umbrella.
Once you have completed a pre-agreed time period on site, you complete a timesheet and pass it on to your Manager to sign.
Submit your timesheet to both your recruitment agency and umbrella, showing how many hours you worked that week/month.
The umbrella company will invoice the recruitment agency, which subsequently bills the end-client.
Once the umbrella company received payment from the agency, they can prepare for your payroll.
Your umbrella will process your payroll, and pay you a salary, following deductions for taxes (income tax + National Insurance), the pre-agreed umbrella fee, and any other deductions (for pension contributions, for example). They will also reimburse you for certain allowable expenses you have claimed – such as mileage.
At the end of each tax year, you can reclaim the cost of any remaining expenses against your income tax bill.