Here are some key things about Ascensions:
1) You lose ALL gold and hero upgrades (and the effect of Abbadon's ability)
2) You KEEP all Achievements, Ancients, Souls, and Gilded upgrades
3) Every unspent Soul you have gives +10% DPS and click damage (additive, not multiplicative, so 20 souls gives +200% DPS)
For farming hero souls you have to keep a couple key points in mind:
1) Every 100 levels you get a guaranteed Centurian boss (one of the special named bosses) which gives extra hero souls based on the level (so level 100 is a guaranteed +1 hero soul every time, for instance).
2) Every boss (5 levels) past 100 has a single chance to be a Primal boss (allegedly this is 25% base), which like Centurian bosses, gives you extra souls based on the level you kill them on, which rapidly increases as the level increases - so Primal bosses start awarding 2, 3, 4, etc as you climb levels. Primal bosses will ONLY APPEAR the first time you go to the stage, although they will stay until they die. Clicking and resetting the stage does nothing, if you had a Primal boss the Primal boss remains, if you didn't there is no chance for one to appear.
3) Centurian bosses also have a VERY small chance to appear instead of a Primal boss - but they ONLY appear once, resetting the stage WILL make the Centurian disappear on anything but a x100 stage.
4) Every 2000 hero levels you get +1 soul, so right before you ascend make sure you get the next 2000 level mark
5) Every 10 levels starting at 100, the FIRST TIME ONLY you beat the stage you are granted a Gilded upgraded to a random hero - this grants a permanent +50% DPS increase to a random hero. Heroes can be Gilded multiple times with the effects stacking additively.
Things you can do with Hero souls:
1) Leave them in the bank to increase DPS. Each Hero soul grants +10% DPS and click damage - additive, not multiplicative, so 1 Hero soul grants 10%, 10 hero souls grant 100%
2) Buy and upgrade Ancients - HERO SOULS SPENT ON ANCIENTS DO NOT GRANT DPS
3) Change which heroes are Gilded - this is COMPLETELY RANDOM, you are paying souls to remove the Gilded upgrade from a hero and transfer it to a new completely random Hero.
Key Ancients:
Each Ancient has their own abilities, but some of them are just TERRIBLE, some are mediocre, and some are completely OP.
1) You are granted a random selection of 4 Ancients to chose from. This selection DOES NOT change with Ascension, it only changes if you buy one or Reroll, both costing Hero souls
2) The cost of Ancients rapidly increases every time you buy one - 1, 2, 4, 8, 16, 35, 70, 125, 200, etc, but Rerolling increases at a much slower rate - 1, 1, 2, 3, 6, 12, 24, 42. So rerolling is a MUCH better option than buying a poor Ancient, especially since there are so many poor Ancients.
3) Each ancient has their own ability and cost to upgrade. Some of them have a max level, some do not, some have rapidly increasing costs, some have static costs all the way
Best Ancients to get:
Morgulis, Ancient of Death - costs 1 soul to upgrade, always has a static 1 cost to level up, and grants +11% DPS additive with no level cap. In other words, he basically changes your Hero Soul DPS from 10% to 11% for each Soul. if you get him early he will make further soul farming go MUCH faster.
Vaagur, Ancient of Impatience - 5% skill cooldown per level, max level 15 (75% cooldown reduction). Arguably the best ancient for farming new levels early. Since cooldowns all feed off of each other, activating them all at once will allow you to beat bosses SIGNIFICANTLY earlier than otherwise (i.e. Clickstorm isn't that great on it's own, but activate it at the same time as Lucky Strikes and it's a massive boost, when you start adding in Power Surge and Super Clicks at the same time it gets ridiculous). Activating every damage cooldown will actually allow you to kill a boss FASTER than the previous level normal monster with no cooldowns.
Bhaal, Ancient of Murder - +15% critical damage. Actually quite good, at least for his first few levels, although his true power only appears when using all your skills at once. Since most of your progression boss kills come from popping Lucky Strikes, Clickstorm and all the damage increasing abilities, this makes +15% critical damage suddenly equal a BIG increase in damage. Since his cost goes up +1 per level, however, his usefulness starts to get significantly less around the 5-10 level range when the DPS you sacrifice would be worth more
Juggernaught, Ancient of Momentum - Gives you DPS based on click count. Actually pretty good, considering how much you end up clicking in the game.
Ancients that sound good but are actually bad:
Some of the ancients are just bad, not necessarily because their ability is bad, but because Hero Souls give +10% DPS each (11 with Morgulis), you have to weigh the cost of the ancient against the lost DPS from the souls. Sadly, a LOT of the ancients are not just bad, but counter-productive to buy.
If they changed the Hero Souls so that you kept the damage even if you spent them almost all of the Ancients would actually be quite good, but the way they have it set up leaves most of them just terrible.
Mammon, Ancient of Greed - +5% gold per level. More gold is bad? I know, crazy right? Mammon has 2 major problems with him. The first is that only giving +5% gold, but essentially costing 10% DPS, even level 1 is simply not worth it. 10% DPS lets you kill monsters 10% faster, which gets you effectively 10% more gold. Buying the ancient only gives you 5% more. The problem is further compounded by the fact that his cost increases +1 per level. So at level 5, you are paying 5 hero souls (50% DPS) for the same +5% to gold. Sacrificing 50% DPS for only 5% gold??? He's just not worth it.
Bubos, Ancient of Diseases - 2% boss life per level. Again, an Ancient that sounds good, but weighed against the Hero Soul cost is simply counter-productive. Especially since his cost goes up +1 per level, the DPS cost of buying and upgrading him is simply NOT worth it. Even at level 1 you are sacrificing 10% DPS for just 2% boss life, at level 5 you are sacrificing 50% DPS for just another 2% boss life. Simply not good.
Argaiv, Ancient of Enhancement - +2% hero damage per Gild. Easy to see how poor it is. You get +2% damage per Gild at the cost of 10% damage (and that's only if you buy him FIRST). Laughably useless and counter-productive at any stage of the game.
Chronos, Ancient of Time - +5s boss timer. Again, sounds crazy right? More time on the boss? Who wouldnt' want that?? Well, because all of the skills only have a 30 second duration. Meaning that extra 5 seconds is only at your base damage. Which quite frankly is laughable compared to your all-skills-used DPS. +5s on a boss you couldn't kill with every skill active equates to MAYBE 1 or 2 % of the boss life - nowhere near worth it for the Hero Soul DPS you sacrifice.
ALL of the +2 second duration bosses. Basically, since each skill isn't very good on it's own, these Ancients are ONLY useful if you get every one of them for all the skills AND the +5 second boss timer - something that quickly gets cost prohibitive.
ALL of the gold skill/treasure chest bosses - should be obvious. They only give gold based on very infrequent occurences - either Treasure Chests appearing or your gold skills being active. Again, the DPS you lose buying and upgrading them would have gotten you more gold.