Groudon is an excellent physical attacker, with its base 150 Attack stat and STAB on Earthquake. However, Ice Beam is quite possibly the most common attack in Ubers, and Groudon, being slow, has trouble switching in to 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. But still, nothing likes switching into its Earthquakes, and it can OHKO those things immune 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 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 Pokémon 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 the least common Uber, compared to Latias, Latios, and Lugia, three of the most common, so you get better coverage than Rock Slide if you have Overheat.
Choice Band Groudon works really well. Hidden Power Bug / Hidden Power Ghost hit Latias and Latios. As mentioned above, Hidden Power Bug will OHKO Exeggutor and Celebi, 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 she switches, and then proceed to Swords Dance. Groudon can continue to Substitute down to the Salac Berry boost, allowing it to outspeed positive natured Deoxys-A. Earthquake gives STAB and will hurt Forretress and Mewtwo after a Swords Dance or two, while Hidden Power Ghost will hurt Lugia, Latias, and Latios.
The 204 Speed EVs allow Groudon to outspeed Deoxys-A and normal Deoxys after the Salac Berry boost, while maximum Attack is obvious on a sweeper. 44 HP EVs will 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, so you can come out vs. something like Blissey, and Roar as they go to Lugia. This will bring in anything but Lugia, which Groudon generally 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 their 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 you 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 in. 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 / win against Kyogre, it 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 your Attack and defenses? You could run a very small amount of Speed to beat other Groudon / Kyogre that also have low Speed. For starter Groudon, you might want to be slower than starter Kyogre, so that your weather overwrites theirs, 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, and survive everything you throw at it save Choice Band Hidden Power Bug / Ghost and then 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 still needs SolarBeam to do anything to Groudon. Lugia can take hits all day with a Reflect up, and can just Toxic stall it to death, or can alternate between Calm Minds and Recovers before killing with Ice Beam. Exeggutor survives everything but Hidden Power Bug and Fire Blast / Overheat, and OHKOs Groudon with Solar Beam (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 Pokémon are the first each battler sends out, the slower Pokémon will always control the weather. This is because the faster Pokémon's weather activates first, but is promptly overwritten by the slower Pokémon's.
If Kyogre switches into Groudon, or vice versa, the weather will change.
If Kyogre and Groudon switch into each other at the same time, then the person who makes the decision last switches in their Pokémon 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, it will report that the weather is still going strong. However, there will be no effect. SolarBeam takes 2 turns, Thunder has 70% accuracy, and no moves are boosted / 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.