There are several different methods of fishing worth trying depending on species targetted and gear used. Firstly I will divide this section into reef fish and pelagic fish.
Reef Fish in the shallows. By shallow I mean 2 - 15m. Most of the Swains Reefs have a lagoon or area of shallower water, usually on their leeward (north-west) side. These shallows have a mainly sandy bottom with patches of reef and bombies (single pinnacles of reef). The main species targetted in these areas are coral trout and red-throats. They tend to move throughout the shallows as well as congregating around the patches of reef.
The technique I use is to anchor on a patch of reef or bombie and hang back toward another patch, allowing for wind and current, but most importantly be actually fishing over sand. Once in position, start a berley(chum) trail, chopped up pilchards are good. If the berley is not drifting where you intend, move. The idea is to draw the fish away from the reef patches and over the sand where they have less chance of running you into snags. These shallows usually have a number of 'fishy looking' spots so it is not too hard to find one where the wind and current can be used to advantage.
Start berleying before fishing. Toss in a handful, then three or four chunks every few minutes. I use a 15kg casting rod with two ganged 6/0's and minimum weight, or ideally no lead at all. If all has gone well with the choice of location you should be hanging over a sandy bottom with reef 30 - 50 m downwind/current with the berley trail creating a line in between. Cast the lightly weighted bait (half a pilchard is good) about 20-25 m back into the trail and let it drift down, freespooling to allow the bait to drift back toward the reef.
The larger fish are usually more cautious in the shallow water and tend to hang back. When freespooling be ready to quickly strike and wind as the fish will rush into coral given any opportunity. If there is no or little result after 20-30 mins try moving and do the same again at a different patch or bombie. The fish generally respond fairly quickly if they are there.
Deepwater (20m+) reef fishing. There is not a lot of finesse in this style of fishing. Drifting is probably the most effective as more ground can be covered although if the wind or current are too strong or if a particularly productive spot is found it may be preferable to anchor.
The rig I use is same as for shallow water except for a running ball sinker of sufficient weight to reach the bottom easily. (most commonly about 4oz/120gm) The advantage of a ball sinker running directly to the hook is it is more snag proof than other rigs. Drifting over coral reef can be costly on terminal tackle. By using a running sinker, snags can often be freed by fairly gently jiggling the rod tip up and down to 'hammer' the sinker on to the hook thus knocking it free. It is important to do this before pulling hard on the snag. With a bit of practice it is fairly easy to differentiate between bites and coral and free the hooks from the minor snags using this bouncing technique.
Another rig used for this type of fishing is the standard paternoster with a fixed sinker (snapper lead) at the bottom and two droppers above. Advantage is having two baited hooks, disadvantages are they are more snag prone with less chance of being freed. They are also more likely to tangle with other lines if there are several people fishing in close proximity. As a friend of mine says, "they are a great way of meeting people" as you can have quite a lengthy chat as you untangle rigs. Nonetheless, in very deep water, or when pickers are bad, or if you wish to try two different baits, a paternoster can work ok.
Drifting baits for pelagics. This is a fun and exciting way of fishing the Swains and the outer reefs although sharks can be too much a pest at the latter. The idea is to present a pilchard,gar etc on ganged hooks (a wire trace is also wise) so it is drifting mid water.
It can be set beneath a float or balloon. A piece of cork works well and can be attached by slicing a groove into it with a sharp knife then sliding the line into the groove 4m or so above the bait. This will break away on a strike which is desirable as other fish will be attracted to the struggling hooked fish and will strike at anything moving in it's vicinity. Many of the common fish at these reefs have teeth that make short work of fishing line. You will obviously need a few spare corks. Cast or drift the bait 50m or so behind the boat then leave the reel in gear with 'strike' drag and either hold the rod or place it in a rod holder or somewhere secure. Strikes are usually spectacular.
Burleying can be helpful, a disadvantage is it also attracts sharks. 'Visual' burley in the form of flashers (a 'daisy chain' of old CD's is good) works well at attracting fish minus sharks. Most of the pelagic fish respond to sight moreso than smell. If constructing a flasher rig, you can be imaginative, I have seen some amazing contraptions. But use wire and make it sturdy, you occasionally get some massive 'strikes' on the flashers. Jigging in the vicinity of a flasher can also be good, more about jigging later.
One other highly effective alternative is to fish live baits, but they can be frustratingly difficult to get hold of when you want them. A bit of burley and bait jigs in the shallows can often provide a bucket of fusiliers which are great for mackeral, or casting small chrome lures around the reef edges may pick up a small tuna, scad or rainbow runner which are perfect big fish baits.
Trolling is one of the simplest methods of fishing these reefs and is probably the easiest way of hooking into a big pelagic fish. Basically it is a case of hanging a lure between 30 - 100m behind the boat and dragging it around. However, as in all fishing styles, if attention is paid to detail the chance of a good catch improve. I refer to trolling from a dory although the same principles apply when trolling from the mothership. Most offshore lures will work as long as they are sturdy and can handle a bit of speed.
Skirted lures, bibbed and bibless minnows are all effective, as are rigged gar,mullet etc. One of each in a 'spread' is good as they cover different depths and fish moods. What works one day may not the next. Three lines can be trolled easily enough from a dory if they are staggered in distance and any turns of the boat are made gradually. I usually run surface or shallow running lures well back with the deep divers fairly close astern. Watch the lines to ensure they don't cross and tangle, reposition the rods if necessary. Troll at 6-10 knots around any features, drop-offs etc especially where there is a good current flow. I usually troll slower near the reef and faster in more open water, both for the species targetted and the safety factor. Upon getting a strike I accelerate for 50m or so, this assists in setting the hook and quite often provokes a second strike on another rod. Retrieve the other lines quickly and if it looks like the fortunate angler who hooked up will be occupied for a while, use the opportunity to drop down a jig, being respectful of where other lines and fish are.
Jigging is a very successful method of offshore fishing and has undergone quite a resurgence recently, largely due to some innovative Japanese designs in tackle. I prefer jigs in the 125 - 180 gm range, these suffice in the usual fishing depths of 30 - 60m and are not as arduous to crank up as the heavier models. Again the method is quite simple, basically drop the jig to the bottom and wind it up fast. Keep contact with the jig on the drop, either with the thumb feathering the spool of an overhead reel or lightly palming the spool of a threadline reel. Strikes often occur on the way down and are usually noticed by the line stopping prematurely or suddenly accelerating rapidly. Clamp down on the spool, put your reel into gear (or bail arm over) and strike. If the jig reaches the bottom begin winding immediately before it snags. My technique is to wind fast for 20m or so, slow for a few metres then fast again with a few flicks of the rod tip now and then to make the lure flash and flutter. Repeat until the lure has reached the surface then do it all over again. Speed is the essence, you cannot wind too fast. A bait rigged with a chin sinker for trolling such as mullet or gar can work well as a jig using the same technique.