Looking at some drawings of ichthyosaurs, it occurred to me that, although they are roughly the same shape as dolphins, they must have had to swim in a similar way. Cetaceans have a blowhole so they only need to raise the top of their head above water. Turtles have a neck, which means they can hold their head up, as could plesiosaurs etc of course.

The streamlined shape of icthyosaurs suggests they moved like dolphins but surely they would not have been able to do that and also breath through their nostrils. They would have had to keep actually lifting their 'beaks' out of the water, impeding their progress.

What is the current thinking on all this?

Great question.  I don't know of any research looking into this.  A quick search seems to suggest they didn't have nostrils, and may in fact have had blow holes, though I can't substantiate this.

I'll keep looking into it and get back if I find anything else.

It is an unresolved question, but the best suggestion I've seen is that of "porpoising," or leaping out of the water at a good speed. If done correctly, it allows breathing at a high speed. According to Richard Cowen, it would allow a physiologic capability similar to a dolphin. http://mygeologypage.ucdavis.edu/cowen/ichthyosaur.html