Here's what Emily and I think it takes for a reasonable and caring NT to establish a good working (or other kind of) relationship with an Aspie:
Firmness and consistency—even more than with most people. Rapid changes, especially if they seem arbitrary, can drive an Aspie out of his mind.
Advance planning. Aspies, as a group, don't take well to spontaneity like “Instead of going to the park this morning like we planned, why don't we get Chinese takeout instead?”
Willingness to converse one to one. Aspies keep track of things, let alone people, best one at a time. Small group conversations can be very difficult.
Conciseness. Aspies take in facts best in all their literal, unvarnished glory, one at a time. So be prepared to give the bullet point version when talking about something.
Ability to go into detail. Remember that the Aspie may not have the background knowledge of the situation that many NTs would. In fact, an Aspie (and probably some NTs) may not even know enough to know to ask a question about something. So, for example if you're going to an event which serves food and which asks for donations to defray the cost of same, make sure to volunteer that fact up front.
Patience with multiple questions. Aspies have difficulty generalizing. For example:
“It's going to be cold that day. Make sure to wear your coat on the bus going there.”
“What about going back – do I also need to wear my coat then?”
“Yes, that would be a good idea too.”
Patience in general. It may take several different ways of explaining something to get the point across:
“How long would it probably take us to get there?”
“Well, you know traffic is tied up that time of day, and especially along the Beltway it's bumper-to-bumper traffic.”
“But how long would the trip be?”
“Well, you take into account that it's going to snow a few flakes, and Washingtonians' collective driving IQ drops heavily when snow is involved.”
“Once again – what amount of time will the trip take? About how many hours?”
“Oh I see. Figure between one hour under normal conditions and an hour and a half or even two hours, tops, if the traffic gets really bad.”
“That long possibly, huh? OK, thanks for the information!”
Tolerance. Not only for the Aspie, but also for many people who won't be quite as kind and understanding as you are. Not to mention a great big dollop of patience will come in handy here too. If, say, you're the Aspie's boss or significant other, people will come to you with complaints, of varying degrees of merit, about things he's said or done.
Individual understanding. AS affects different people in very different ways. Your Aspie friend, worker, lover, etc., is still an individual and needs to be treated like one, not like a generic prototype. Not all or even most Aspies can do the same things or need the same accommodations. For example, some Aspies have no problem with public speaking, while others find it a major effort even to get out of the house.
Last but not least, a whole bunch of kindness and love never hurt.