Groudon is an excellent physical attacker with its base 150 Attack stat and STAB Earthquake. However, Ice Beam is quite possibly the most common attack in Ubers, and Groudon, being slow, has trouble switching into a lot of things. If you can take Lugia down, though, this makes a good stallbreaker. It can support Sunny Day-style teams with its ability, but SolarBeam isn't that good in Ubers, and Fire isn't particularly good, either. Still, nothing likes switching into its Earthquakes, and it can OHKO those things immune to them with a Choice Band attack for the most part.
Overheat is used to kill Skarmory and Forretress and can also be used to kill Exeggutor. It's used over Flamethrower and Fire Blast because Flamethrower fails to OHKO all but Forretress if Groudon doesn't have Special Attack EVs and Fire Blast has less accuracy. Fire Blast can be used to avoid the Special Attack drop, but you almost never need it for multiple Pokemon on the enemy's team. Use Hidden Power Ghost with Overheat and Hidden Power Bug with Rock Slide generally, although you can use Overheat with Rock Slide if you want. Hidden Power Ghost fails to OHKO Exeggutor on the switch in, though, so beware of that. Other than that, however, Hidden Power Ghost and Hidden Power Bug both hit Latias and Latios equally hard. Hidden Power Ghost also hits Lugia, so Rock Slide isn't as useful. Rock Slide hits Rayquaza, Lugia, and Ho-Oh. For a single physical supplementary attack, however, Hidden Power Ghost is usually used over Rock Slide and Hidden Power Bug because it hits Latias, Latios, and Lugia. Ho-Oh is much less common than Latias, Latios, and Lugia, three of the most common Ubers, so you get better coverage with Overheat than with Rock Slide.
Choice Band Groudon works really well. Hidden Power Bug and Hidden Power Ghost both hit Latias and Latios. Hidden Power Bug also OHKOes Exeggutor and Celebi however, while Hidden Power Ghost will not. Overheat really rampages through Skarmory, Forretress, and Exeggutor. This means Hidden Power Ghost eases up predicting the switch to Lugia and also does more to stuff like Rayquaza and Ho-Oh should you not predict them coming in.
Groudon can come in on the likes of Blissey, set up a Substitute as the opponent switches, and then proceed to Swords Dance. Groudon can continue to Substitute until it gets the Salac Berry boost, allowing it to outspeed positive natured Deoxys-A. Earthquake gets STAB and hurts Forretress and Mewtwo after a Swords Dance or two, while Hidden Power Ghost hurts Lugia, Latias, and Latios.
The 204 Speed EVs allow Groudon to outspeed Deoxys-A and normal Deoxys after the Salac Berry boost, and maximum Attack is obvious on a sweeper. 44 HP EVs mean the Salac boost comes on the third Substitute, and the additional 8 EVs are relegated to Special Defense.
Only use Roar with a few layers of Spikes down. Once you have these in place, you can send Groudon out versus something like Blissey and Roar as they go to Lugia. This will bring in anything but Lugia, which generally means something Groudon takes on fairly well. This set completely walls just about any Blissey, non-Calm Mind Lugia, and physical Deoxys-A. Toxic can be used to actually do something to Lugia, and then you can Rest off its Toxic and use Earthquake to keep Blissey from coming in and using Aromatherapy. The EVs given make Choice Band Metagross's Meteor Mash a 3HKO but still leave Groudon with some attacking power.
Counter can be used to kill other Groudon and the common Choice Band Rayquaza, but Groudon and Rayquaza aren't really the most common switch-ins to Groudon. Groudon can use Substitute to block Knock Off and Toxic, as it cannot be broken by weaker physical attacks or Seismic Toss. Groudon can use Thunder Wave to paralyze Latias, Latios, and Lugia and then kill them with paralysis + flinch by pairing it with Rock Slide. Don't use Eruption; it's absolutely horrible.
For the Substitute versions, you will want 404 HP; it's nice for Blissey and Deoxys-D. Sweeping Groudon can have max Speed for the tie or win against Kyogre, which can help a lot. Another option is little-to-no Speed. Groudon is tied for slowest Uber in the game with Deoxys-D and Kyogre, and most Ubers like to hang out at 307 Speed, 1 above Groudon's maximum. If Groudon won't be beating them, why not just power up its Attack and defenses? You could run a very small amount of Speed to beat other Groudon and Kyogre that also have low Speed. For lead Groudon, you might want to be slower than lead Kyogre, so that your weather overwrites its, possibly even using Brave and lowering Speed IVs to 2 (with Hidden Power Bug) or 3 (With Hidden Power Ghost). Regardless of what you do, you will want a lot of Attack EVs unless you are running a stall set.
Checks and Counters
Latias and Latios are immune to Earthquake, resist Fire, survive everything Groudon can throw at them save Choice Band Hidden Power Bug or Ghost, and can OHKO with Ice Beam (but Groudon with Special Defense EVs survives and can go for the 2HKO). Flygon works, but is very specific and won't do much to almost anything else, and it still needs SolarBeam to do anything to Groudon. Lugia can take hits all day with a Reflect up and can just Toxic stall Groudon to death, or it can alternate between Calm Mind and Recover before killing with Ice Beam. Exeggutor survives everything but Hidden Power Bug, Fire Blast, and Overheat, and OHKOes Groudon with SolarBeam (watch out for a Rayquaza switch-in to defend against this). Kyogre somewhat... you won't want to switch Kyogre into a Groudon Earthquake. If Groudon is faster and has a Swords Dance on the switch, Kyogre will get OHKOed, unless Kyogre has 404 HP (252 EVs) and 276 Defense (240 EVs).
Controlling the Weather
In a match-up of Kyogre vs. Groudon, if both Pokemon are the first each battler sends out, the slower Pokemon will always control the weather. This is because the faster Pokemon's weather activates first, but is promptly overwritten by the slower Pokemon's.
If Kyogre switches into Groudon or vice versa, the weather will change.
If Kyogre and Groudon switch in at the same time, then the person who makes the decision last switches in their Pokemon last, thus dominating the skies. In matches where a person has a limited amount of time to move, this can cause the players to try and play chicken, waiting until the clock is as close to running out as they dare before punching in the move and praying the connection doesn't lag.
Rayquaza / Golduck
If Rayquaza or Cloud Nine Golduck is out, the game will report that the weather is still going strong. However, there will be no effect. SolarBeam takes two turns, Thunder has 70% accuracy, and no moves are boosted or weakened. If Kyogre or Groudon switch into Rayquaza, Air Lock will still be in play. Once Rayquaza leaves the field, the weather returns to normal.