Original post here
Take a look at http://forum.egosoft.com/viewtopic.php?t=295990 - lots of good advice there. The last post (mine, currently) contains some pictures that may well help.
Of course, the easiest way to get an Aran is... by using another Aran (with appropriate equipment, natch! 
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SAVE OFTEN!
Be prepared: Start from the sector where you want to end up - a nice safe sector with an EQD and/or shipyard such as Kingdom End would be good. Docking computer, triplex scanner & transporter device (all good to have) have a chance of being destroyed upon entry to the UFJD sector, so have backup with a duplex scanner as well. Take some Asats, a couple of extra 1- or 2GJ shields & some good fighter drones (Mk2 or Keris) with you, as well as top-whack marines in Engineering & Mechanical (if you're not using boarding pods). Fighting skill isn't really important WRT the capture itself - it's the same chance as any other abandoned ship. I use low-fight-skill grunts for Aran hunting to train them up.
Drop an Adv sat when you enter the sector. Press 'k' to give you the satellite camera view superimposed on the sector. Zoom /in/ & scroll through anything on your radar screen, in both X/Y & X/Z axes, looking for the distinctive radar 'shadow' of a huge cigar/submarine-shaped object (ie long, straight with slightly pointed rounded ends. [Trust me, once you've seen one you won't mistake it for anything else!]) You'll notice that this method centres your view on the highlighted (but not necessarily targeted) target, giving you a better chance to spot an Aran hiding behind a 'roid. Then max zoom out & take another look on both axes. /Then/ Target (not highlight) a far-away 'roid or something, zoom out with the f3 camera & take a final visual look around, all axes - you're looking for a yellow submarine a long way off in space, all lit-up!
Some people find it helps to have <playership> moving when looking around like this: it helps to distinguish between <playership>'s shadow & something else. If you're going to do this remember to do it on autopilot, 'cause crashing into a dark sector's 'roid you've not seen because you're concentrating elsewhere is funny only for the rest of us . If you're lucky enough spot an Aran, SAVE! Fly to it & drop another Asat nearby before you do anything else. SAVE!
NOTE: According to the code posted in a long-ago thread there is slightly less than a 2% chance of an Aran being generated in a UFJD sector unless that sector has a gate, in which case the chance is zero. So if you see a gate, broken or otherwise, forget it. The Aran (or Goner Ranger; you'll only get one /or/ the other, & since the Ranger is tiny you've almost no chance of spotting it) can be generated a /looong/ way off (I've seen unconfirmed reports of up to 120Km) & this figure is not limited to the ecliptic, so don't be surprised if you can't spot one visually
This may sound complicated, but the easiest things always take the longest time to explain. Once you get used to the method it may take 15secs tops; on average, most likely around 5-10sec. for the whole 'scan sector' routine. If there's nothing else visible, target your satellite!
If you're really lucky you'll have no hostiles in the area; this will give you some more time to use SETA repair, or not if you've plenty of time or don't want to fiddle about. If you've got the game music turned down, turn it up for this exercise: it's easier to judge by listening to the music change when the Aran turns hostile than by listening for the single 'hostile ship nearby' bleep, especially if your gaming area is subject to 'noises off'. Eject from your ship & use the repair laser to turn the Aran hostile. Did I say SAVE!? If you've no hostiles at this point you can repair the hull some more now - you won't know how badly damaged it is until you've successfully boarded it; IIRC it spawns with between 2% & 23% hull.
If you have hostiles IS, be patient. The Asats you've dropped will give you warning, by being destroyed even if you haven't been watching their screens. Your drones have a limited lifetime, so judge carefully when you want to release them: the hostiles may take a while to realise you're there. By default on release drones are set to 'protect (player) ship'; since the Aran can't shoot back you /should/ be OK, but if you've taken damage (say from nudging the Aran by getting too close by accident) they'll prolly attack it, so watch yourself here! SAVE!
Send your marines in. In-ship or out, either by the 'Piracy' command, or 'Launch all marines'. In the menu you're presented with, there should be an option 'board nearest..' where the Aran should show up. I've experienced a boarding with a Kraken where the K wouldn't lock onto the Aran - it always went for the nearest Xenon (whether boardable or in view or not); no idea what caused that!
SAVE! before the marines get to the hull. SAVE! at every point. Hull-cutting should be OK if using BPs as they cause little damage, but if you're using an M6 you should be prepared for some frustration at every level. /This/ is why you need top-level marines in mech & eng: they cause as little (or even no) damage as possible whilst doing their jobs.* If your hackers fail you can always pick them all up & send them in again, if you have time
Once you've managed a successful board, SAVE! Then transfer the extra shields over first, so they gain some extra recharge time. If you need to dock manually to transfer kit, do so carefully! Obviously, if your DC has survived that's the easiest, quickest & safest way to dock. Once docked, you can transfer the JD & necessary ecells & jump right out back to the sector you started from. Once you get there, SAVE! The last thing you need now is for some stupid NPC TL or capship (or anything else if you have no shields) to blunder into you!
You'll end up in more or less the position IS where you jumped from, so if you started a long way from your Aran's intended (first) destination, be prepared for a long wait!
* ISTM that fight skill determines how long a marine section takes to deal with each deck; mech (or engineer, I always mix those two) skill determines the damage done whilst doing so. I've no idea if the skills are interrelated or interconnected in any way - ie whether the team causes more damage because it's stayed longer because of the lower fight skills, etc. However this is all limited speculation - if anyone wants to take it further, please start a new thread!
Good grief, I didn't know I'd absorbed /this/ much info about Arans - thanks everyone!
Hope this helps! - X3:TC 3.x vanilla applies