If you work by the hour, a time log is the start of your invoice. What you do not record, you cannot bill.
Recording hours
Note per day the customer, the duration and what you did. Do it right after the work; a phone is enough. You can enter hours as 1:30 or 1.5.
Invoicing
Select the hours you want to bill and put them on a draft invoice with your hourly rate. You see the lines and the amount, adjust them if needed and finalise the invoice. The hours are then marked as billed, so they never end up on an invoice twice.
The VAT
The invoice charges VAT on the amount and the booking ends up in your VAT return by itself. Need a correction? Then use a credit note.
You can also keep your mileage in the same place, so you have everything for your customer together.
This guide is general information, not tax advice. Check the current rules for your situation with the tax authority or your bookkeeper.