If I live somewhere with no background imagery and have no GPS device, what's the best way that I can contribute?

In addition to the other suggestions:

• You could add POIs (Points of Interest) like shops, restaurants, schools etc at existing streets. It is ok to make a rough guess at their position first, e.g. “halfway between these two intersections”. You can improve existing POIs by adding names and opening hours.
• Maybe you have other mappers nearby who do have GPS equipment. See your user page on osm.org for a list. You can check the contributions of those looking still active and see if they have uploaded any tracks. Then you could split up work: The GPS guy records the tracks and uploads them. You would trace them and tag the data.
• If you feel you want to contribute to the greater cause of OSM but not necessarily in your local area, you can turn to HOT and help trace aerial images for humanitarian purposes.

One Possibility is to try Walking Papers. You can print a certain area and then draw features on the paper. When you are finished, scan it and digitize. It will not be as accurate as when using GPS, but it is still better than not having any details at all on the map. You (or someone else) can still improve the data later, when better equipment is available.

what can be useful if you map by this method: add a tag fixme=resurvey or something similar, so that other users know that the data might not be accurate. There are even users who systematically look for these tags to go out and improve it.

http://walking-papers.org/

Do any of the Truckers use gps or sat nav? maybe emailing them ( web addresses could be sign written on the trucks) for traces and telling them something about OSM. Locals could them add addresses for the benefit of all. Does anybody fly over? in aircraft or balloons could they take pictures? would the government supply any help? after all it is a step towards prosperity and trade. Glider flying clubs could be asked as a source of Ariel pictures as well.

You should forget about contributing to OSM. Take up a different hobby like producing invisible art or alternativly, produce invisible maps ???? They would be better than some of the efforts I've witnessed recently and I'm sure you would definitely find someone to sell them to.