Bahamas has numerous airports of entry with customs & immigration eg Freeport & Nassau (of course) plus Marsh Harbour, Treasure Cay, Spanish Cay, Bimini, Chub Cay, Andros North, Andros Town/Fresh Creek, North Eleuthera, Great Exuma etc etc
A few have an FBO. If you're flying into one that does I recommend you use it. It's well worth the twenty bucks or so for the one-stop much reduced hassle dealing with customs & with immigration. You'll also be able to pay by credit card at an FBO, otherwise it's cash only for customs & for immigration.
Generalities:
It's the pilot's responsibility to make sure US C & I are notified at least 1 hr prior to your inbound ETA at your airport of entry.
Only Freeport & Nassau are towered. Nassau has radar, Freeport is procedural. All the others use 122.8. Most of them *don't* have parallel taxiways so backtracking is the norm as is using opposite departure/arrival runways (wind permitting). Broadcast your intentions. A lot.
Radio terminology is similar enough to US procedures that you shouldn't have trouble. A few differences eg 'Line up & wait', not 'Position & hold'; 'Runway zero niner' not 'Runway niner' etc.
If you can, submit your return plan into the USA before departure (plans accepted up to 23 hrs prior to ETD). Ph Miami 1 866 347 0316 or +1 305 233 2600. It can be a pain in the arse trying to do it from customs/immigration in the Bahamas. OK if you're at an FBO there. Your return plan will need to be either IFR or DVFR. If DVFR make damn sure you activate it & get a customs TXDR code prior to crossing the ADIZ. If IFR you'll be transferred to Miami in the normal way if departing from Freeport or Nassau, otherwise call them directly with your position/altitude, departure time & IFR request.
Except at FBOs you will have to deal separately with customs and with immigration. Even if they're in the same room at adjacent tables. It seems they're often incapable of handing paperwork between themselves.
Avoid arriving or departing before 0900 & after about 1700 or 1800 to avoid overtime fees from customs AND again from immigration. Weekends & public holidays also attract o'time fees. Some places even charge double fees if you arrive/depart in the overtime hours *and* on a weekend.
If you're flying into a non-customs airfield you'll need to clear customs in & out of the Bahamas at a customs field & complete a 'transire' form in duplicate before you can depart on your domestic leg.
Specific fields.
If flying into Freeport you will need to submit an arrival report & a Bahamian flight plan form for departure to the Flight Service person behind the glass screen next to C & I. Weather is available in the portable building next door.
At Nassau hand it to one of the FBO front counter people & they'll submit it. Nassau FBOs have a radio in their briefing rooms to call ACD for a clearance. It can take up to 30 mins or more to get it so better to call for the clearance indoors then board rather than board & wait in a hot aeroplane for it. BTW, Nassau ATC is useless as tits on a bull so expect delays & inefficient handling.
It can be quicker at Nassau to use the FBO on the terminal side of the runways (Jet Centre? Can't remember) although I think Millionaire is a bit nicer. Millionaire is stuck in a corner on the other side of the runway complex & often has traffic jams in & out of the ramp.
Marsh Harbour has an FBO called Cherokee Air. Well & truly worth the relatively few extra dollars to go there & avoid the zoo at the terminal building at the East ramp. Cherokee's ramp is about half way down the runway which conveniently avoids backtracking the full length of the runway if you need to take-off using 09.
Treasure Cay has no FBO so you're stuck with C&I. A couple of the C & I ladies there are really nice to deal with. People tend to land using 14 & take off using 32 to avoid lots of backtracking.
Spanish Cay is a private island but if you're taking people in there then no worries. They have their own C & I lady. Sometimes she's in her sub-office on the field, other times it's her main office at the marina. Fly over the marina usually gets someone's attention to come and get you in a golf cart. Watch the runway carefully, it's used as a road by the golf carts.
Chub Cay's C & I person is often not in his/her office. Fly over the marina & s/he'll come out when they can. Most I've waited is 45 mins.
Bimini, Andros North/San Andros) & Andros Town/Fresh Creak have no great surprises other than the backtracking thing.
North Eleuthra has an FBO (from memory. I know there's one down there somewhere because I've used it. Just can't remember exactly where.... )
Paperwork:
You'll need 3 copies of your General Declaration (GenDec) with your pax names & DOBs for both directions. Prior to departing the Bahamas you'll hand the return ones to Bahamas Customs to be cleared out. ***Make sure you get one stamped copy back!*** You'll need this one to hand in to US customs.
Each pax will need to complete Bahamian Customs cards (a white card) for arrival into that country. They're available when you get there but they prefer you have some already.
Each family (same surname) at the same residence will need to complete a US customs form (a blue card) for entry back into the US. A crewmember need only complete a 'Crew Declaration'. If you don't have one then a US blue card works too. Just a bit more to fill out for the crewmember. They're available online for printing at the US customes website. I think they used to be available at the NBAA's website too.
A 'transire' is a form used in the Bahamas to declare any freight or cargo you're transporting between islands. It's to do with their taxes & duties. If you don't have any cargo you'll still need to complete it in duplicate but state on it that there's no cargo.
The crew must have his/her pilot's licence * medical ***as well as*** an FCC restricted radio operator licence. You can do the FCC one online at the FCC's website.
The aircraft must have its paperwork too. Radio licence etc.
There's probably other bits and pieces but that's what I remember of the top of my head.