What happens when wifi channels overlap?
Solution 1:
First it's a bad idea to use a channel other than 1, 6 or 11. Channel 1 is 22 MHz width so it interferes with channel 2 and 3, and similarly channel 6 interferes with channel 4, 5, 7 and 8. See more http://en.wikipedia.org/wiki/List_of_WLAN_channels.
It's better to set both access points on channel 1, than Carrier Sense Multiple Access with Collision Avoidance will be used. CSMA/CA is a system that regulates which sender may send his packet, letting them take turns in a polite, organized manner: from the header at the start of each transmission, the others can see how long the transmission will last. To use CSMA/CA the access points must be on the same channel. See Wikipedia link: http://en.wikipedia.org/wiki/Carrier_sense_multiple_access_with_collision_avoidance and http://www.cisco.com/c/en/us/products/collateral/wireless/aironet-1250-series/design_guide_c07-693245.html#wp9001231.
If channels 1 and 2 are used, Carrier Sense Multiple Access with Collision Avoidance cannot be used. Now they will interfere with a lot of packet loss.
Solution 2:
There is no "intelligently", if you have 2 networks on the same channel or on channel that overlaps this make interference between signal of different network. If others network are quite far there will be low interference and it will still work almost correctly but if the different network are too close interference will be high and you will get slower throughput and higher packet loss.
It's better to have a network on channel 5 and one on channel 6 than both on the same channel, this will reduce interference
Usage of channel 1, 6, 11 and 14 (14 is not allowed in most countries) or 2, 7, 12 or 3, 8, 13 or 4, 9 or 5, 10 guarantee no interference but if you need more channel because of channel used by neighborhood using 3/8 or 4/9 with 1, 6, 11, (14) is "better" than adding 5/10 or 2/7
Solution 3:
There are technologies on the market that allow the same wireless channel to be shared intelligently by multiple networks, but these aren't commonplace yet and mostly apply to wireless N networks.
For instance, with multiple antennas, one can use beam forming to reduce (uncontrolled) interference and make better use of the channel capacity. CSMA (Carrier-Sensing Multiple Access) is another technology/technique used to intelligently share a single wireless channel. AFH (Adaptive Frequency-Hopping spectrum) is a related means of channel-sharing that is increasingly employed.
As wireless technology becomes increasingly prevalent, I think we'll see more and better implementation of coexistence technologies (which are already employed in wireless technologies like Bluetooth and especially cellular communication like CDMA and EDGE networks) since there's only a finited radio spectrum and both industry and the public are becoming increasingly dependent on wireless communication.
Edit: Since I originally wrote this answer, Wireless N has since become much more popular, and these technologies are obviously much more widely accessible.