If one were to browse among all the serious books and websites looking for advice on carrying a gun in one's purse, probably the most common piece of advice one would find is “Don't.”
And that's generally my advice on the topic, too. Off-body carry is so fraught with problems that the simplest advice is to just avoid it if possible. But that's not realistic. With some combinations of dress, body type and firearm, it's purse carry or nothing at all. Honestly, if I'm carrying a purse, which is rare these days, it's got a gun in it even though my usual Glock is on my hip. At its heart, a purse is a bag over your shoulder to hold useful things you might need, right? A gun is a useful thing you might need. QED.
So, if someone's going to do it anyway, the best thing to do is to examine the shortcomings of purse carry and work to mitigate them from the start.
First and foremost, a gun in a purse is just less secure than a gun strapped to your body. Purse theft and purse snatchings happen all the time, but when's the last time someone had her belt stolen by someone running by on the street?
If there's a gun in your purse, you have to treat it like it has the nuclear launch codes in it, although maybe don't go so far as to handcuff it to your wrist…but keep it close or under lock and key at work. Keep it well inboard in restaurant booths and do the trick with the chair leg through the strap when seated in chairs. If you're the sort who occasionally forgets her purse, purse carry is likely not for you.
Guns in purses tend to not be as accessible, especially with what trainers Craig Douglas and Cecil Burch refer to as “In-Fight Weapon Access,” or “IFWA” (because everything needs an acronym). It's important that a purse be designed to carry the firearm, with a separate compartment holding a properly sized holster that covers the trigger and is affixed to the interior of the compartment. This is both for safety, since it prevents a roll of breath mints or a mascara tube from getting inside the trigger guard and turning a trip to the department store into a memorable experience, and to ensure that the gun is always oriented where your hand can find it.
Regarding accessibility, a carry purse can have some advantages in certain circumstances. For instance, it's perfectly possible to walk through a dark parking lot with your hand actually on your gun, while to a casual onlooker, you're just hugging your purse close to your body. I know this has been reassuring to me at several times in the past, including a memorable time when an elevator lurched to an unexpected stop in an otherwise deserted parking garage at 3 a.m. All was well that ended well, but having my hand unobtrusively already on my gun was a comfort.
Personally I prefer purses with hidden gun compartments held closed with hook-and-loop, and disguised in a pleat or seam, but that's because I don't have to worry about little hands going where they shouldn’t. The presence of kids changes everything, and the only way to have a gun in a purse then is if the purse has a locking zipper that remains locked. This dramatically diminishes the accessibility of the firearm to the point where it's just a nice thing to have if you run out of gas or have a flat tire. Also, the whole “treat it like it has the nuclear launch codes in it” factor goes clean off the charts.
To sum up, I really don't think it's the best idea, and I discourage purse carry for the most part, but if it's between that and being unarmed, well...Know the limitations and the weaknesses and work around them them with quality training, practice and equipment, like anything else.