One rule of thumb I've heard is to get them sharpened every five ice times. This is for the average skater who is at a decent skill level. But it depends a lot on how hard you skate and how sharp the blades are to start with. If you go practice hockey stops for hours on end, you'll wear your blades down faster. If you get your blades sharpened to a small radius (i.e. sharper than average), then the blades will become duller more quickly.
It really depends on what you start with. A 5/8 cut will go pretty quick but a 7/16 will last longer. This does not apply to kids however. I swear my son must be walking on rocks by the way his skates get nicked up...
You may consider spending some time trying different cuts: 5/8, 1/2, 7/16. You will notice more "bite" with 7/16 but it can take some time getting used to how deep it is (makes it harder to stop if you are a beginner).
If you can't figure out when to get it done, just bring them in every 10-15 skates and try out the range of cuts. Eventually you will settle on what works for you.
For me, I now use 5/8 because it gives me the edge I want without the break-in period. Now I take them in about every 10 skates. If they get beat up, I'll take them in sooner.
The one thing I've learned as a relatively new player is that it is better to over-sharpen than under-sharpen.
I know its a matter of personal preference. Some people like going a whole season without sharpening - some sharpen after every game. I personally believe, however, that a beginner needs a good grippy edge while they are building confidence in turns etc.
There is nothing more discouraging than trying to get the hang of a tight hockey turn and losing your edge every single time. Even with full pads, falling all the time sucks.
On the other hand, a good skate edge means you get the technique, balance and weight transfer down first. You have no choice but to quickly understand how the dynamics of your edges work when they're cutting and not sliding.
Once your muscles "get" the movement, its much easier even on duller skates.
This is just my own experience, of course, and others may disagree, but personally I wouldn't go more than 10-15 skates without a sharpening until you develop more of a "feel" for when its time.