First Step: Tanks and Heals
You'll need to see if there are any tanks or healers on! If you don't have these, you can't do anything, so.
Open up your guild panel and look specifically for any class that can tank or heal: warriors, priests, death knights, paladins, druids, etc.
Right now, you're just seeing who's on, not asking anyone yet.
Second Step: Check Levels
Who meets the level criteria for your instance? Remove anyone from your mental list who isn't at or above the right level.
Third Step: Check Locations
Where are they? A person's location tells you what they're doing almost as well as whispering them.
A city usually means auctioning or leveling a profession or just standing around bored. Feel free to ask these first as they're the most likely to go.
A world zone usually means leveling or helping someone else. Feel free to ask these but they usually don't want to go -- people in world zones are most often specced for dps and focused on leveling.
If someone is in a raid or instance, they definitely can't do anything right now! But it also means they're interested in instancing and might be willing to run something with you when they're done. Feel free to whisper the tank or healer in an instance and ask if they're interested in running your instance after theirs. If you're very lucky, someone will be leaving their group anyway and they'll slip you in.
If someone is in battlegrounds, they're either grinding honor or killing time. Feel free to ask them. If they're in arenas, definitely don't bother them. They need to focus.
Just focus on tanks and healers for now. Don't fret if people say no, or if someone isn't the right spec. Just be polite, keep moving down the list, and keep an eye out for anyone logging in.
If you can't find a tank and healer, you can try pick-ups. Most people would rather not instance than do this. The options are to pug or to give up for now.
Fourth Step: DPS
If you do find a tank and healer, go ahead and ask for dps in guild chat. Dps is the easiest part of the group to fill in because they're the most common. To play fair, I generally invite the first to speak up. If you don't want to take someone in particular who's on, then just whisper the dps you'd be willing to take. More time but less drama.
Fifth Step: Trouble-Shooting
Problem: Everyone's too busy.
Solution: Schedule for a time when they aren't busy.
Problem: They aren't the right spec.
Solution: Offer to pay for two respecs (one to switch and one to switch back).
Problem: They don't like that instance and will never ever run it.
Solution: Find another person or pick another instance.
Problem: They want to run a different instance.
Solution: Compromise and run both.
Problem: No one's on.
Solution: Find out when tanks and healers will be on and try to get in touch with them before then to schedule something. Best resource for information is your guild forum, an officer, or just plain ol' gchat. This is usually more of a scheduling issue than a lack of resources. Half of my guild's tanks and healers don't log on until 10:30pm EST. If you find out when they're most available and arrange your runs around when it's convenient for them, you'll be golden.
Problem: Everyone's on but no one will go.
Solution: Depending on why people won't go, try other avenues. Someone focused on leveling is unlikely to want to instance either now or later, but someone who's just tired of instancing today (or is busy with arenas) will be a likely candidate later. Try and pin down when they're available and either pre-schedule them or try again at that time.
People focus on one thing at a time. Most people are unwilling to change their focus if they're on a roll with something they want to do, but that doesn't mean their focus will never change. To make it easiest on yourself, you need to probe into the following:
- Schedules. When do people log on? Log off? It's pertinent to know how much time they'll be staying on and how pressed for time they are. People with no spare time have none to give.
- Goals. Some goals don't include instancing at all. Others include it under certain circumstances. Being willing to fulfill a goal with your group will get you an automatic member.
- Specs. People often change specs -- find out when and why (including plans for endgame) and either catch them at the right time or make it worth their while to change it for you.
- Reliability. You can do all the legwork to plan something, but if the people you ask aren't reliable, it's a disaster in the making. Some members will show up on time and prepared based on a simple verbal agreement. Others won't. Keep going back to the people who prove they won't let you down, and keep sampling your guild for more reliable people.