How to avoid procrastination during the research phase of my PhD?
I have found (and continue to find) two kinds of strategies that have some success in preventing me from procrastinating.

Silly, but scarily effective:


As silly as this might sound, implement a blocker like Leechblock or Chrome Nanny and block sites that you waste time on. I used to scoff at such things, but once I installed them, I found myself being forced to spend more time working. 
Along the same lines, disable email alerts. Once I did this, I found that I could spend many hours working without getting distracted by random emails. 


Less silly, and also less effective

Much of the procrastination when starting research in grad school comes from the lack of clear structure (as you indicate). So the trick is to create structure. For example, if you're working on one problem, and you've spent a little time generating a few ideas, write them down, and methodically start working through each of them one by one, going as deep as you need to go in order to test out an idea. When you're doing so, try to forget about the larger problem, the context, your Ph.D, your future career, and all other "big picture" matters.  

More likely than not, the idea won't pan out (most don't!). In that case, move on to the next one. 

The problem with early-stage research is that it doesn't look like you're making any progress, so it's easy to slow down and waste time. But if you can measure progress not in terms of "papers published", but in terms of "ideas tried", you'll get some sense of the amount of effort you've put in, and that can help motivate you to try more ideas, and so on. All these failed ideas are teaching you valuable things about your project, and they will eventually be useful because of what you've learnt.