To read a text as you would one in a modern language - look up words when you need to in order to understand a passage, learn what you can from context, etc. Do your best to read instead of translating - those are fundamentally different activities.

I'd like to reiterate that using interlinear translations or Loeb editions wasn't a contraindicated practice, per se. There are just certain problems inherent in the practice that we were advised to look out for. It is certainly a useful tool sometimes.

I think what it all comes down to is what I mentioned above: reading a text and translating a text are fundamentally different. Both require you to interpret a text, but translating a text - particularly an ancient text - require you to interpret it in more and in different ways. So if you're relying heavily on a translation to understand a text you're using tools that mediate between you and the original more than, say, a reference grammar and a lexicon.