(Note that businesses can offset their VAT liability with the VAT they paid for services/goods received.)

this is misleading, it's like saying you can get a salary as a worker. you get the salary. there is no "you can"

the same is true for VAT, the amount you owe is the difference between the tax you paid for the service/goods you bought and the tax you collected when you sold.

at the end of the month or what ever other period you are required to pay taxes the sum is simplified this difference.

with a VAT rate of 25% if you paid something 125, (100 base + 25 vat) and sold it after for 150 (120 base + 30 VAT) you owe the (30-25) = 5.

In the accounting software the tax rate for every line item is entered when creating the entry. So at the end of the month its easy to make a report.