Great question! I'll be looking closely at the answers.
So far, I've usually laid out all the cards in a spread face up. Then often said something about what first came to my mind when I looked at the spread. I then go from card to card, usually starting with #1 of the spread through to #last. I also often jump from card to card if I see connections while I'm moving through the spread (especially jump back to cards I already said something about). When I'm through with all cards, I take a "step back" and look at the larger picture and mention anything that strikes me about the relationships between the cards. I try to end up with a short summary and suggestions about actions the sitter could take.
In reality, all of this bleeds into each other, I often jump here and there, depending on what the person I read for says and/or what I notice (what pops into my mind) as I go along. Often, I feel as if a spread starts making sense only after I've started to speak, I literally don't see many things when I'm just looking and not communicating. (In online readings like the exchanges here, it works the same way, only with writing. No matter how many notes I took when I laid out the spread, it all comes together only when I start writing it out, when it is addressed to the final recipient of the reading.)
I suspect that some more obvious structure might be more helpful to face-to-face sitters, but sometimes get carried away by all those connections and associations that keep coming at me. (In online readings this doesn't matter that much because I can edit things into a structure before I send anything.)
My main problem is determining what should be said and what is too much information and serves to distract and confuse instead of helping to clarify (this is not tarot-specific, though, I generally have a tendency to speak in a baroquely meandering style). How do you people know what to say and what to leave out? How do you know what's just your imagination going wild and what's actually "the message" coming through?
I have been experimenting a bit with turning the cards over one by one, to prevent the jumping around, but I often feel as if I lack the big picture at first then. That's why I like Alta's technique of purposely looking for patterns first and then digging deeper where it seems most interesting/valuable. I shall try that one out. Thanks for the suggestion.