Kea,
An agent will arrange viewing and all the submission of documents for you. Of coz, u will need to pay the agent's fee as well. Once u confirmed a unit you like, u will hv to make an upfront deposit maybe $500 - $1000, tis amt will depend on how much the owner wants first.
Then there is a "window period" I can't remember is 7-14 days in case the deal is off. The property agent will then fix a first appt for you, and you will be required to submit all the necessary documents, HDB will then processed the sale of the flat and according to the price, they will calculate the max loan/tenure you will be taking. They will work out a calculation for you.
Then on the 2nd appt it is the handover of keys and the final payment to the owner (the amt above valuation minus the deposit). If you really need it urgently, can ask HDB to expedite but it's on case by case basis also. The whole procedures take about 3 mths or so