Some people quit completely after the first day. Some have a transition period. Some don't entirely quit, but rather cut smoking down a lot. Depends on you. Smoking habit is a very complicated addiction, and while nicotine is a large portion of it, it may not be all of it for you. Hopefully you got a model that actually vapes well and works right. Some a really great, some not so great. With most you will probably cut down dramatically right away.
Another issue is nic level, and this is very hard to gauge based only on how much you smoked. Too much variation in actual smoking methods to be able to say, and nic absorption from vaping is not the same mode as smoking. A good middle of the road value is 12-15 mg initially, and cut back if it is too much, or increase it if it is not enough. Often the act of vaping itself in the beginning is so convincing and effective that you actually don't realize you are not getting enough nic to keep certain withdrawal symptoms away, and these often show up 2 - 4 weeks after switching.
Remember ecigs are NOT meant to be a smoking cessation device. They are meant to be an alternative to smoking. Many do quit entirely, but some do not. Still, in that regard, they have a much better track record than typical products, like gums or patches. Everyone is different, so I will hesitate to tell you my personal experience, as many new users will compare themselves with me and then kick themselves if their experience is not the same. There are no rules or promises here. I can say that it is highly likely you will cut down smoking dramatically without thinking about it. That seems to be pretty much universal. 70-80 % quit entirely, but not necessarily immediately. A lower percentage find vaping is not enough, and either still have a few real ones a day, or try smokeless products, like Swedish snus. They are not necessarily weak or without enough will power. Its a very complex chemical, physical and behavioral addiction you are trying to control, and is different for everyone.
I found in the beginning that being involved with ECF, PV technical info, making my own juices, and basically investing both time and money into vaping, rather than smoking, really helped keep me clean. The key is to have fun with it, relax, don't be hard on yourself if you don't quit right away, and enjoy! No matter what the rhetoric is on whatever website/ad for your ecig is, vaping is NOT a magic bullet for everyone. Statistically its a pretty good one, though.
Learn to use your PV properly, keep it in good, clean operational order, vape as much as you want in the beginning. Don't vape higher than around 36 mg ever, but don't worry about whatever level under that that keeps you sane. You will know if you have had too much, as you will feel nervous and sickly. Drink lots of water if your juices have a lot of PG in them, as it will dry you out.
Best of luck, and enjoy the vapage!