If you are getting into fashion, especially if you are interested in retail (retail, e-commerce, buying, merchandising...) one of your industry must reads has to be Drapers. It is a smart choice to be in the know of all market trends even if you are a designer. If you want to make decisions for your shop or design consciously towards a market that is affected by trends, and here I don't mean fashion trends, but social, economic or even legal/political then Drapers is really a must.
Because I have been going to different fashion schools in London for the past 5 years, I can tell you that all fashion business classes start with "read Drapers".
Drapers is a fashion retail business weekly in print (£4.75) and online (to what you can subscribe to access for £199/year).
Of course there are many other things you can read for industry updates such as Women's Wear Daily (WWD) which is based in the US, and discusses everything from fashion trends to news to business. You can also visit WGSN, which is online trend forecasting agency. They are the best for trends online, but its membership only, where you have to apply and pay (forgot how much, but these trend forecasts are usually super expensive starting around thousands for a season). I was lucky to have access because fashion universities here get a student access to it so they can experience and learn how to use this sort of information to their advantage. If you live in a city where there are big fashion magazine shops then you can also visit these to flick through the pages of other forecasting print magazines (these are more like very expensive books).
Do you know of any other fashion business print or online magazines that you'd suggest others to read?