You'll spawn on a detention centre. If they don't let you rebuy your ship there, don't panic. If you didn't or couldn't pay your fine there, take an Apex to the nearest place with an interstellar factor(or related station) and pay your fines. Now walk over to the Inter Astra place and rebuy your ship.
Wherever your ship was blown up, it will have to be delivered to that station you're now on. If the Express Lift says there's no ship available, go check in the the Inter Astra folks and you'll see your ship on a delivery timer.
Note: Once my ship was delivered it still wasn't available via the lift. Had to go back to Inter Astra, swap ships and then swap back and now it's all good.
I'm only posting this because I couldn't find this answer anywhere and I just about lost my mind thinking I missed out on my rebuy and lost my fully-eng'd ship. Hopefully this will save someone the time it just took me to figure this out. No prompts in game at all for what the hell to do. Yeesh.
Edit: Added delivery timer information and note. o7
