The burn-out timer starts with your first hack as mattozan said and is 4 hours.
Hacking without mods
Hacking at 08:00, 11:00, 11:05, 11:10 will lock the portal until 12:00.
Hacking the portal at 12:01 will be successful.
Hacking at 08:00 and then waiting until 12:00 will also result in refreshed timer and hack amount, meaning that 4 hacks will be available again, not only 3.
If a portal has, say, Common Multi-Hack (+4 hacks) and you hack it 3x at 08:00, 3x at 09:00 and someone destroys the multihack, portal goes automatically into burn-out state.
Likewise if a portal is burned-out and you place a Multi-Hack on it, you will be able to hack it immediately - the burn-out state gets postponed.
- Knowing all this can be 'exploited', especially when a farm* is planned.
Say a farm with RMH, 2x RS + turrets/force amps is planned at 12:00. All players will visit the place and hack all the portals once at 09:00. This will activate the burn-out timer, which refreshes portal's hackability at 13:00. At 12:00 players assemble again, build up the farm and start hacking. Rare Multi-Hack give +8 hacks = total 12 Hacks. 1 hack was already made 3 hours ago, so it is 11 hacks left. After 55 minutes the 11 hacks are done and portal goes into burn-out state, however it's by the time the burn-out timer kicks in and refreshes the hackability of mentioned portals, giving players another 12 hacks.
= Total of 23 hacks with only 1 Rare Multi-Hack
*a Farm is a local community's 'event' at place with high density of portals. It's basically when a group of players levels up portals for the sole reason of obtaining items from them. They keep on hacking them until they burn them out, or until their inventories are full. The farm is usually of a certain level and when mentioned in chat, players use the term F8 there and there. If there are some multi-hacks or heat-sinks used, the notification could be as follows F8 2xVRMH VRHS, or when 1 last player is needed F8 1xR8 missing.
CMH, RMH, VRMH = Common / Rare / Very Rare Multi-Hack
RS = Rare Shield
VRHS = Very Rare Heat Sink
F8 = Farm of level 8 portals
R8 = Resonater level 8
A8 = Agent level 8