I agree with Ganidiirsi for the most part. The primary targets of a boarding action will be Engineering and Bridge (including the computer section) and enemy senior officers.
In HG combat enemy ships are often left without maneuver drive or fuel (especially from the "Fuel Tanks Shattered" Interior Explosion result) and must be captured after the rest of the enemy fleet has been driven off. Usually such ships are also low on weapons (from lots of Weapon-1 hits) and low on crew (from Crew-1 hits on the Radiation table). These hulks, if captured and repaired, could make nice additions to your own fleet.
Step Zero is to summon the survivors (if you can reach them) to surrender. This saves a lot of time and fuss. You keep this up all the time. Every enemy you don't have to kill is one more you can interrogate or trade for your own guys. This depend on just who you're fighting, of course.
Step One of a boarding action is to remove all remaining weapons that don't need power (missiles and sandcasters). Fighters might be very useful for this, or other armed small craft. Obviously you do this while trying to minimize additional damage to the prize. One creative ship designer build a Marine Assault Ship that carried Modular Cutters with battlefield meson guns in the cutter's module. These battlefield meson guns were just the thing for plucking off any remaining turrets. They were also very useful for providing fire support to the boarding parties as they advanced into the ship.
Step Two is to get the Marines inboard. Exactly how this is done depends on YTU. The wreck is usually tumbling and so you have to stabilize it first. You can use magentic fields, or grappler arms, or "thumps" from low-powered repulsors; whatever you want to have work in YTU. I have seen HG designs for 50kton Assault Ships that have thousands of tons of displacement allocated to "grapple arms" for just this occasion.
In unusual situations (unusual being defined by the GM) the wreck might not be stabilized before sending in the Marines. This would be very risky and require high skill on the part of the small craft pilots and the Marines going over. I think this would be done only if it were really, really necessary.
Once the wreck is stable, over go the troops. If you grappled the wreck, you're close enough that the Marines can just float over in their battledress and combat armor, using small EVA thruster packs to maneuver (Marines should practice this a lot). If you used some non-contact method to stabilize the wreck, the Marines approach in small craft, and then go over in their armor with the thruster packs. I can't imagine that a battle-damaged ship would have docking ports or hangers that could be used, especially for the first wave.
Once the Marines are on the hull, they find a weak spot to break in at. Airlocks are good, maybe fuel scoops, sensor arrays, holes in the hull from battle damage, that sort of thing. You pick spots close to your target areas, if you know the layout of the enemy hull. If not, you go aft for the engines and in the middle of the hull for the bridge (on big warships I can't imagine putting the bridge up at the pointy end, AHL notwithstanding).
If the Marines have to blow their way into the hull, they'll use special explosives (that really exist) called line charges. Think of a shaped charge that is made into a long rope of explosive with a flat side. You make a circle of the rope with the flat side in contact with the surface you want cut and fire the thing. It acts like an instant cutting torch all along its length and works instantly. Remember the hatch blowing open in the boarding action in the very first STAR WARS movie? It'd work like that, but even faster!!! You can also use fusion cutting torches or laser cutters if you want to in YTU. Whatever is needed, the Marines will have along with them. Probably each platoon will have a team of four Marine engineers along with all kinds of fun toys.
Once inside the Marines advance carefully and by the numbers. The point man serves to locate resistance by drawing fire. I don't think any sensors in the armor will be all that useful inside an enemy ship that is in vacuum and has lots of battle damage. Whatever use the Marines can get out of their sensors they will, of course. When resistance is found it is suppressed with grenades and FGMPs. The Marines will not be at all shy about outflanking serious resistance by blowing more holes in the hull or in adjacent bulkheads. If those battlefield meson gun-carrying Cutters are available they will be used as needed.
Then comes the really fun part.... When the Marines get to an area of the ship they want to take without doing too much more damage (Bridge, Engineering, Computer section), the grenades and FGMPs get put away and the gauss rifles, ARLs, and (IMTU) cutlasses come out.
Now, IMTU, the battledress Marine boarding cutlass is not some wimpy little steel blade. It's not even crystaliron. It's superdense metal with a monomolecular edge. It costs Cr2000, weighs 5.0 kg, requires a minimum strength of A (10) and has an advantageous strength level of E (14) which means a Marine probably has to be wearing powered battledress to make full use of it. The cutlass has a penetration of 15, raised to 20 when used at the advantageous strength level. It otherwise behaves as a regular cutlass. All the other Marines wear the standard Marine cutlass IMTU, which is like the battledress one but sized for non-powered people, costs Cr 1500, weighs 3.0 kg, requires 8+ in STR, with advantageous STR of 12+, having a normal penetration of 10, raised to 15 with advantageous STR. I am using STRIKER rules for combat, obviously.
Once the ship is secured, prisoners are put under guard and/or transferred to another ship, the Navy tries to repair and man the prize, and the Marines go home and polish the nicks out of their cutlasses.
Any questions?
