There's no set amount of time because some people are more open than others and a lot depends on how much you see of each other and in what context.
Scientific studies suggest that it takes between 6 months and 2 years for the honeymoon period to wear off, and after this you are able to view the person more accurately rather than seeing only what you (and they) want (you) to see.
Someone who sees a new partner 1x a week for 6 months will probably not know someone as well as the person who sees their new partner pretty much every day for 3 months. However, you could spend two weeks constantly in each other's company and if you are in a little bubble in which the normal trials and tribulations of work, family, DC and family life aren't intruding, that could be less insightful into a person's true colours than a few hours in a stressful situation. It's all so variable.
If you're trying to assess someone there are a few things you can check for. The so-called waitress test emptychairs refers to is a pretty good one for starters. There are lots of websites out there about red flags in dates which contain great advice.
IF you want to be more specific to him and whether he's right for YOU, I'd say don't make the mistake of thinking you really know him until:
? You've had your first disagreement (not necessarily a row as such, but simply a subject on which you have completely polarised views. If it's personal to one or both of you, so much the better as it will be a more genuine indication of what he'd be like to live with). Is he able to agree to disagree? Can he make his point without belittling yours? Does he let you talk without interrupting you? Does he sulk afterwards?
? You've spent some time at each other's houses and seen his approach to domestic tasks. If you cook, does he volunteer to wash up? Does he leave things lying around your house and expect you to pick up after him or is he respectful of your belongings and space?
? You've been together long enough to experience a few plans scuppered at short notice because of whatever reason. How does he handle those? If he's cancelling it, is he apologetic and considerate? If you break a date, is he understanding and sympathetic and keen to see you again?
? You've talked about his attitudes to women and the sex industry. This is usually better if it comes up naturally - e.g. "I was on MN today and there was a discussion about how sexist that song by Robin Thicke is because.... What do you think?" Mens' attitudes towards women can become very clear when discussed in a context like this. Porn is another important topic because if you hate it and he loves it, or vice versa, it WILL cause problems in your relationship. Best to get it out in the open straight away - preferably before either one of you attempts to give the 'right' answer because you don't want to threaten the relationship over something you secretly think is insignificant.
? You've talked about your approach to money. Ideally you'll be the same. It's not impossible to make it work if you have completely different styles, but you do need to understand each other's approach and work out how you could manage that so that it doesn't cause either financial problems or frustration.
? You've talked hypothetically about marriage and children. There isn't a right or a wrong answer to this and talking about it hypothetically doesn't mean it has to happen. Saying "I want to get married when I meet the right person and have children" does NOT mean "I want to marry YOU and have your babies NOW".
Good luck with the new man. Most of all, remember that if it's not fun, it's not worth it. In the meantime, enjoy.