It took my sister six months. A friend of mine did it in a month. Girls in my dance classes, anywhere from a month to a year.
There really is no “normal” amount of time. It depends on so, so much. Some people are naturally relatively loose, but don’t stretch easily. Other people are initially very tight but as soon as they start stretching quickly become flexible. In things like splits, it also depends on things like how your hips are positioned.
Basically, it might take a long time. But don’t be discouraged if it does. The best thing you can do is stretch every day — at least 30 seconds per stretch, no more than 5 minutes at a time, making sure to stretch all the muscles, and both sides equally. Most importantly, don’t be discouraged by other people’s success stories. If you see other people bragging about their two-week split, chances are that whether or not they know it, they aren’t “normal”. They might have abnormally loose muscles/tendons/ligaments, abnormally placed hips, or even some creepy genetic mutation that makes them really flexible (like me).
Also keep in mind: front splits are one thing. Your middle split will almost certainly be very, very, hard. I know maybe two people who easily got their middle splits. It took me around six months to get my middle split without losing it every other day, and my hip sockets are literally shallow to the point of dislocating. When doing a normal split, you are simply loosening all the tissues. To get a middle split, you essentially need to loosen your tissues enough to loosen your joints — to the point of basically pulling them out slightly. Creepy, but also very, very, hard. So if you get your side splits, and move on to your middle split, don’t worry if it suddenly takes much, much longer. Worry if it doesn’t take long enough — it might mean you aren’t “normal” ;)