Pantheon has the one of the highest base movement speeds in the game at 355, tied with Master Yi. Use this and his ranged harass from Spear Shot to whittle your opponents down in lane optimally to take full advantage of his strong early game.
Since using Aegis of Zeonia to stun an enemy also refreshes Aegis Protection, he can easily and reliably avoid the first turret hits when diving. This also works well against physical abilities that apply on-hit effects such as Parrrley, Mystic Shot, and Bladesurge, or turret attacks. This will not block physical abilities like Volley or Ace in the Hole.
Using Grand Skyfall to assist your allies across the map can quickly turn the tides of battle, putting your allies at an advantage.
While in mid air from Pantheon'sGrand Skyfall you can select a target for Aegis of Zeonia and when you land, you will jump at the target stunning from a larger distance (est. 1300) than the standard range (this may be a glitch).
Grand Skyfall makes him one of the best jungle gankers in the game, since he can ignore ward coverage.
Having Exhaust and Flash as summoner spells, along with Heartseeker Strike as your first skill, make for an effective first blood combination when in a side lane with a partner. Those summoner spells also provide two good escape mechanisms.
Getting a Manamune is a good alternative to a Chalice of Harmony for Pantheon since it solves his mana problems and gives him a decent amount of attack damage.
Grabbing a Tear of the Goddess as early as possible will ensure you can stack the mana quickly.
Building an early The Brutalizer can solidify his early lane dominance and help you take your lane opponent out of the game.
If you find your opponents are escaping you too often, or you're being focused down, a Frozen Mallet will give you some additional durability in fights, and ensure that fleeing opponents are slowed after using Aegis of Zeonia to engage them.
Investing in a Chain Vest or Cloth Armor early can help you mitigate his damage output.
Buying health can help you to survive to one or two combos, but you're going to need health regeneration or life steal to sustain yourself in lane against him. After two combos early game, he can be without mana so he shouldn't be a threat.
When laning against Pantheon, play defensively instead of aggressively. Pantheon may be squishy but his damage output is very high early game.
Pantheon has no escapes. Baiting him to attack you and having an ally appear to help is likely to spell his doom without the use of summoner spells to escape you.
Additionally, Grand Skyfall can be used to escape when being ganked (or counter ganks) if you realize it beforehand.
As Pantheon can cast Aegis of Zeonia on you while dropping down in Grand Skyfall and then have it land from outside its normal, using dashes and escapes to avoid Grand Skyfall may have you stunned nonetheless. If you expect to survive his initial burst damage after being stunned, save your escapes for after that instead of getting away from Grand Skyfall. Of course, avoiding the damage from Grand Skyfall all together may be a larger concern - but consider the possibility.
Try to avoid the center of Pantheon'sGrand Skyfall so you don't suffer the full damage of his ultimate.
Avoid laning against him if your champion relies on being on low health to reap the full potential of the champion (such as Olaf and Tryndamere) as his Certain Death will cause him to do a lot more damage to you at low heath.