As a contractor you with need to fill in and submit your timesheets to the client and potentially the agency to record the hours/days you have worked at the client site.
Logging your time
Depending on your contract you will need to record the hours/days you have worked and submit this on a weekly or monthly bases.
Once your timesheet is submitted, typically the client (usually by your line manager) will sign this off.
When you start a new contract you should always establish who will be responsible for signing your timesheets and who will do this if your line manager is away.
Don't run into the situation of falling behind on your timesheets as a lot of clients find it critical for their project planning for contractors to keep on top of their timesheets and submissions. In turn this will affect when you get paid also.
Submitting your timesheets to your agency
Agencies tend to have different approaches to submitting timesheets. Sometimes they may have their own system that, once your timesheet has been approved by the client, you must sign into and upload a screenshot of your approved timesheet with the number of hours/days worked for their records. Others may directly link to the client timesheet approval so you do not need to do anything more with your timesheets. Or in rare cases, they may still be using paper based timesheets in which case you will need to photocopy the signed timesheet and send it to them.
You typically need to submit your timesheet in a fixed time window to make sure you get paid on time and DO NOT MISS the cute off date or you will need to wait until the following week/month.
Invoicing
A limited company contractor will typically send the agency an invoice with the total hours/days worked for that week/month. If your company is VAT registered you should include the net contract fees for the period and include the VAT amount (contract fees + VAT payable).
An umbrella company will usually involve submitting your timesheet to the umbrella company and they will invoice the agency on your behalf.
Payments
You should read your contract carefully and review the payment terms and conditions of your contract. Often agencies pay weekly, within 7 days of receiving your invoice. If you have a limited company this is usually paid via BACS into your company bank account. If through an umbrella company the agency pays the umbrella company and the umbrella company will forward on payment minus fees and deductions.
You should use an online timesheet and invoice management system such as TimesheetHours.com to make sure you do not fall behind or forget to submit any timesheets/invoices to your client and agency.