Shipping times depend on what shipping method you are using.
If you ship your product via regular China mail, then it will take up to 45 days until a customer gets his product.
However, some countries (US, UK and some more) have e-packet shipping option available which is much faster and usually takes up to 20 days.
Finally, you can check if AliExpress can ship directly from the country you're selling products in. Go to AliExpress, select your "Ship to" country and then "Ship from" country as in this example: http://take.ms/efPVd. In such case, products could be shipped even faster.
Let me now if you need any more help!