In what year does It Follows take place?

The straight answer to your question is that It Follows does not take place in any particular time.

In an interview with The AV Club, writer/director David Robert Mitchell discusses the origin of the story being a recurring nightmare of his from childhood:

I’d had this idea for a long time. It came from a nightmare that I had as a kid—this basic idea of being followed by something that can look like different people and only I could see it. It was very slow and always coming for me.

Because of this, he wanted to keep the timeframe ambiguous, while also making the events seem a little dream-like. When asked by The AV Club about the time period and "shell-phone" shown in the movie, Mitchell had this to say:

There are production design elements from the ’50s on up to modern day. A lot of it is from the ’70s and ’80s. That e-reader cell phone—or “shell phone”—you’re talking about is not a real device. It’s a ’60s shell compact that we turned into a cell phone e-reader. So I wanted modern things, but if you show a specific smartphone now, it dates it. It’s too real for the movie. It would bother me anyway. So we made one up. And all of that is really just to create the effect of a dream—to place it outside of time, and to make people wonder about where they are. Those are things that I think happen to us when we have a dream.