Generally, each team has one jungler, which means that there will be one lane of two, and two lanes of one. Since the middle lane will always be a solo lane, this means that top and bottom will have varying numbers of champions, depending on the lane.
Top is usually considered a solo lane because the bottom lane is closer to Dragon, an important mid-game objective. Dragon is hard to solo for most non-junglers, and by keeping 2 champions in the bottom lane, it becomes quite viable to 3-man Dragon after a successful gank (or simply a double-kill). While top lane is closer to Baron Nashor, it takes quite a bit more effort to kill him - more than 3 champions in the early game can probably afford to put out. By the time Baron becomes available, the game is usually nearing the end of the laning phase, after which the difference between top and bottom lane is moot (because all 5 champions are roaming).
With a top solo lane, the champion has a leveling advantage and the potential to farm more minions (simply because there is no allied champion to compete with). Additionally, one must consider that if the other team does not have a jungler, they need to be able to successfully last 2 vs. 1. Most often, this means champions with good sustainability are better suited to the lane, such as Cho'goth, Mordekaiser, Vladimir, or Nasus.
Conversely, there are some champions who do not do well in a solo lane - these tend to be support champions like Soraka, Sona, or Janna who perform much better with a partner to buff/shield/heal. These champions usually go to the bottom lane to ensure that they are in a 2 vs. 2 situation.
In instances where there is no jungler on either team, both top and bottom will have an even number of champions. In this case you may be asked to "switch lanes" not because one lane is "better suited" than the other, but because switching lanes means changing which enemy champions you're fighting (and presumably, have been dying to).
Best Answer
To counter Jayce you have to understand how he works, the best and shortest answer I can give you is, To learn how to counter Jayce - top lane, play Jayce - top lane.
The thing with Jayce is unlike most other character's set of 3 skills, he in fact has a 7-skill-long combo-chain, and each skill in the combo is a different ability. It's also important to note that each of his skills (except Transform) operates its cooldown seperatly for each mode (Melee or Ranged).
To understand what he can do lets look at his skills:
What does this mean for you? It tells us that Jayce can, at the maximum of once every six seconds (the cooldown on his ultimate: Transform), gain a short but signifigant boost of speed, which makes him a decent sprinter.
What does this mean for you? He has a basic damage dealing Q-key skill on a relatively short cooldown. Keep in mind he can hit you with this and then transform and hit you again with it immediately.
What does this mean for you? He can passivly regain his mana while farming in melee mode, sustained with a passive aura of magic dps from time to time or he can hit you with a very quick burst of attacks in ranged mode. The ranged version of this becomes more threatening as he gets stronger, particuarly when on-hit effects become involved, but should never be underestimated regardless of level.
What does this mean for you? Combined with his spammable Q-Skill, he can throw in this decent nuke as well while in Melee Mode or Set himself up for either a chase or quick escape in ranged mode. This spell is a real problem if your playing a good Jayce, as he can both use the knockback to get you off him defensively and set you up for a gank offensivly. Good Jayces will surprise you by jumping to you with the Melee Q-Skill, running past you just a step, and then knocking you into their tower with the E-Skill.
It is first important to say that this skill costs no mana. So basically, on top of having the ability to transform between modes, doing so gives him single-use-per-change basic attack bonuses. This means that he will want to transform as often as possible to take advantage of these bonuses, regardless of which mode he may seem to prefer.
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Now because of his unique play mechanics, Jayce has the ability to employ an entirety of (or partial if he wishes) 3 nuk'ish skills, a burst attack speed buff, a move speed buff\nuke boost, a passive aoe dot ability, and either a armor and magic resist debuff or additional small nuke, for mixed magic and physical damage, in any order he pleases, in a decently fast amount of time.
Given Jayce's skillset, to counter him you should pick heroes that can endure a great deal of punishment by means of outlasting their opponent's harass. Top-lane heroes that can do this include, but are not limited to:
How do these heroes counter Jayce?
Irelia, Renekton, Tryndamere, Jax, and Poppy are capable of producing burst dps strong enough to take down Jayce before he can finish his combo. Irelia and Olaf both have a nice share of true damage which can help even more to this end.
Irelia,Renekton, Tryndamere, Olaf, and Jax all use mechanics that in one way or another make them stronger as combat prolongs. This means the longer of a combo Jayce wants to employ to you, the stronger you become, increasing your chances of coming out of the skirmish on top.
Renekton, Udyr, and Jax all have extremly low cooldown stun moves which can inturrupt Jayce's chain of spells and throw him off-balance, effectivly shutting him down.
Yorick and Alistar both have low cooldown skills that heal them in some way. Which gives you sustain to endure his combo chain.
Irelia, Poppy, Alistar, Renekton, Jax, and Tryndamere all have some sort of jump or dash skill which can get you back into the fray when Jayce attempts to knock you out of it with his E-skill.
Poppy and Alistar both have skills that can knock Jayce around the battlefield which can also inturrupt his chain of spells and throw him off-balance, effectively shutting him down.
Several other heroes might also fit the bill but these ones seem to do it the best, good luck!