Some basic recommendations:
Hacks get progressively more difficult. Ship Design Hacks exponentially so. You can probably pull off the first one with no more than a fleet bodyguard but it depends. Main factor: Special Forces Patrol, #of previous hacks, interplanetary threats (interplanetary munitions booster, raid engine, dire guardian lair), and various minor factions/AI Plots. If you have the Hunter plot on or a Special Forces Commander AI then I'd be afraid to hack.
Send in fighters to clear tachyon sentinels, send in a MK2 Science Vessel (comes cloaked), select the ARS tab of the science vessel, and then use the galaxy map's note tool to write down the three choices. Then I pull the science vessel back to where I need more K - since I often play with Spire Civilian Leaders and the Dyson sphere, there are usually a couple places I can use a cloaked knowledge gatherer.
The leftmost listing on the ARS tab is what you'll get if you don't bother to hack, like zoutzakje describes. After the hack is complete and the planet is under your control, you can click on one of the three ARS tab selections from any research lab present in the system (including the ARS itself) to unlock it. Note that in co-op, one hack allows each player to choose their unlocks separately, so player A can get more Younglings and player B can get their favorite Sentinel Frigates.
If you do a lot of hacks, it may help to capture the system next to the ARS, clear the ARS system of mobile fleet ships, send in a mobile builder, and set up a small beachead with some repair, shields, turrets, and maybe even a space dock.
A small caveat: moving the Ship Design Hacker will reset the hack timer. This is not fun when you're a minute from completion.