Ask before your first date ends (recommended). This is the least stressful way to ask for a second date.
If both of you are having a good time, just be honest and ask.
You could say something like, 'You know, I find you an interesting person and would like an opportunity to talk with you again when we have more time.
Would you be available this Saturday morning for breakfast or would Monday night be better?'
If your date says no to both offers, you have choices depending on how much you like your date.
If you decide to ask after your first date, you'll have to do it by email or phone if you have their number. Of course if you see them on a regular basis you can suggest a second date in person.
If you're asking on the phone or by email you could use the same format. Simply refer to a second date as an opportunity to 'chat some more'.
Always offer two choices. If they decline both, offer one more option or suggest that they call you.
You could also say that you'll call them back in a few weeks when you're not as busy. It all depends on how badly you want to see them again.
What is a nice way to say 'no' if someone asks you for a second date?
Always thank them and mentioned that you're flattered they want to go out with you again.
Tell them that you'd like to be friends but are not interested in dating. (that's a nice way of saying don't call me anymore)
Quickly changed the subject before they have a chance to think about what you said. Then make an excuse to end the conversation as soon as possible.
It all depends on how well your first date went and how convenient it would be have a second one. i.e. if they live close by, a second date would be easier than if they lived far away.
Sometimes people are nervous on a first date and not themselves. Often people will relax and be more calm on a second date. Also if your first date was only a few minutes it's not enough time to get to know each other.
If you feel that your first date has potential, by all means it might be worth your time to go out again. On the other hand if you know for a fact they aren't what you're looking for, why waste your time? Politely decline an offer for a second date and look for Mr Right somewhere else.