How and when do banks give interest on savings accounts?

It depends on individual banks. There are different variants of interests.

Upfront Interest Fixed Deposit

Usually this involves putting a sum of money for a fixed period i.e. 2 years for 2% and the interest would be credited in your bank account the very next day after you open the FD account. This essentially earns you higher than 2% because you are able to grow the interest paid out.

Yearly interest payments

DBS and POSB savings accounts of 0.05% have interest credited once a year.

"Interest on Savings Account is calculated on Quarterly basis. The following formula is used by DBS Bank to calculate interest on Savings Account.

Monthly interest=Amount (Daily balance)(No of days) Interest/Days in the year"

Monthly interest payments

This category would be similar to the likes of Singlife / Stanchart Jumpstart account and OCBC Frank account. Interest is credited on a monthly basis which is a good thing because essentially interest is somewhat compounded, hence your interest per annum if you calculate based on your initial capital (without any new transaction) would be higher than the indicative interest rate.

Interest rates are per annum. E.g. 2% p.a.

But it is calculated daily (some banks use average daily balance) and credited monthly.

For simplicity sake, assuming 1st May your account have $10k till 31st May, the interest credited will be $10k x 2% × (31/365).