I know. You're expecting something brilliant here, maybe a flow chart or a strategic Malcolm Gladwell video.
Wrong post. I'm simply going to tell you how to start looking like a global manager or employee even if you're locked in to Peoria as your home base 100% of the time. The basics to get started - check it:
Rule #1 to looking global: ALWAYS DO THE MATH FOR THE PEOPLE YOU TALK TO RELATED TO THE TIME ZONE THEY ARE IN. That's actually rule 1-5. Being global, or even being bi-coastal in the states means that the people you talk to should be comfortable that you're dependable, accessible and in many ways, just like the people they're talking to across the hallway.
That means you don't tell them, "let's meet at 1pm" - and you're referring to 1pm your time. Or even say, "let's meet at 1pm my time". You want to be on their team even though you're not there - DO THE MATH FOR THEM. Especially if you're requesting the meeting or are the leader.
Time zones mean friction. You job with remote folks is to take friction out of the system. Make them want to work with you by at least taking the time zone friction off the table.
Rule #2 to looking global, even when you're not: Don't do all the meetings with people in time zones other than yours at times that are simply convenient for you. I can't say it any better than my friend, Gerry Crispin, who laid out the following comment on this post of mine over at Fistful of Talent:
"Don’t make weekly calls of your team (matrixed or not) at times convenient for you simply because you are the team leader. Spread them around and get your tail out of bed at 3am on occasion."
Gerry actually has some deeper comments about working with a global team, so check them out on that post.
But, this post is about the basics. You can't possible do all the cultural things you'll need to do in a global spot before you have the moxie and selflessness to do the math for the people you're trying to schedule.
Walk before you run. Then maybe your company will talk to you about that spot in London. Or, maybe Lithuania might be a better fit for you.