The spell slow hobbles it's victims:
Creatures affected by this spell are staggered and can take only a single move action or standard action each turn, but not both (nor may it take full-round actions).
So creatures can't take full round actions. However, I'm unsure how this affects (if at all) round long casting time spells like Summon Monster that have a casting time of 1 round.
Does it not affect the spell? Stop victims of slow casting it at all? Or does it take twice as long?
Yes, you can cast a spell with 1 round casting time while slowed. It will take 2 rounds.
From "full-round actions" section:
A spell that takes one round to cast is a full-round action.
From "standard actions" section:
The "start full-round action" standard action lets you start undertaking a full-round action, which you can complete in the following round by using another standard action. You can't use this action to start or complete a full attack, charge, run, or withdraw.
Both quotes are from How Combat Works page at paizo.com.
When the spell takes effect is not an easy question to answer, at least as far as RAW is concerned. I think that we can assume that we can’t apply an effect until we know what the effect is. And here comes another reasonable consideration.
To cast a spell, you must concentrate. If something interrupts your concentration while you're casting, you must make a concentration check or lose the spell. When you make a concentration check, you roll d20 and add your caster level and the ability score modifier used to determine bonus spells of the same type. Clerics, druids, and rangers add their Wisdom modifier. Bards, paladins, and sorcerers add their Charisma modifier. Finally, wizards add their Intelligence modifier. The more distracting the interruption and the higher the level of the spell you are trying to cast, the higher the DC (see Table: Concentration Check DCs). If you fail the check, you lose the spell just as if you had cast it to no effect.
(emphasis mine, source: Magic page on paizo.com)
So, while the caster concentrates on casting the spell we can not know the effect for sure. It can be either normal effect (if the spell is cast successfully), or no effect (if the concentration is interrupted).
How long should the caster concentrate then?
The interrupting event strikes during spellcasting if it comes between the time you started and the time you complete a spell (for a spell with a casting time of 1 full round or more) or if it comes in response to your casting the spell (such as an attack of opportunity provoked by the spell or a contingent attack, such as a readied action).
(emphasis mine, source: Magic page on paizo.com)
Returning to the "start full-round action" description
The "start full-round action" standard action lets you start undertaking a full-round action, which you can complete in the following round by using another standard action.
(emphasis mine, source: Combat page on paizo.com)
So, the action (and thus casting the spell) is complete after you have performed the second standard action. It means that the following rule
A spell that takes one round to cast is a full-round action. It comes into effect just before the beginning of your turn in the round after you began casting the spell. You then act normally after the spell is completed.
is not applicable in this case. Apparently, it applies only when the spell takes a full-round action, not two consecutive standard actions.
Thus we have to rely on the general rule for spells with long casting times.
A spell that takes 1 minute to cast comes into effect just before your turn 1 minute later (and for each of those 10 rounds, you are casting a spell as a full-round action). These actions must be consecutive and uninterrupted, or the spell automatically fails.
(emphasis mine, source: Combat page on paizo.com)
It is given as an example, not as a general rule, but this is all we have for spells with casting time longer than 1 round.
So, it looks like you have to start concentrating on your turn in the first round then continue through the second and finish on the third right before your turn. And at that point the effect is resolved.
