SamKuker101 covered the high points: you need at least 100 gold (which on Impossible can take a while) and the more fame you have, the more and better heroes you attract.
Some heroes will show up even if you have no fame: Brax, Gunther, Zaldron, B'Shan, Rakir, Valana, Bahgtru, Serena, Shuri and Theria. Others need 5, 10, 20 or 40 fame; those which require 40+ fame are called champions.
The fewer heroes you have, the more likely one is to stop by. Your chances of this happening go down with each hero you have. At the start (with no heroes and <25 fame) your base chance is 3% per turn. This goes up as you add fame, if you're Famous (your chances double, although they never go above 10%) and/or if you cast the spell Just Cause (which adds 10 fame while in effect). It drops back to 1% chance per turn (2% with Famous) as soon as you add that first hero, though.*
Summon Hero will randomly call any hero needing no more than 20 fame. Summon Champion brings you those heroes otherwise requiring 40 fame. You may also find heroes as prisoners, especially on Myrror. In any of these cases, you don't have to pay these heroes to join, nor do they care what your current fame is.
A very few champions require you to have Life (Elana and Roland) or Death (Mortu and Ravashack) spell books. The Life spell Incarnation is the only way to summon Torin the Chosen, probably the best single hero in the game.
Best bet? Learn and use Summon Hero as soon as you can. Especially if you already have your first hero.
*The complete chart, as found in the official strategy guide:
1st Hero: 3% at 0-24 fame; 4% at 25-49; 5% at 50-74; 6% at 75-99; 7% at 100+.
2nd or 3rd: 1% at 0-24 fame; 2% at 25-74; 3% at 75+.
4th or 5th: 1% at 0-74 fame; 2% at 75+.
6th Hero: 1% at 25+ fame.
All chances are per turn; they double with the Famous skill, but can never go above 10%.
It's not spelled out anywhere in the guide, but I believe there's a bias toward those heroes for whom you've met the minimum fame requirement. In other words, once your fame exceeds 40, it's unlikely (if not impossible) to be randomly offered a starter and far more likely (and perhaps exclusive) for you to see a champion.
Post edited July 16, 2013 by TwoHandedSword