How to search for a public POI by name

Here's an example searching for Avis 

http://www.mapquestapi.com/search/v2/radius?key=<YOUR_KEY_HERE>&origin=1015%20museum%20circle%20jacksonville%20FL&radius=30&hostedData=mqap.ntpois%7Cname%20ilike%20?%7Cavis%25&maxMatches=25&ambiguities=ignore

breaking it down
http://www.mapquestapi.com/search/v2
The base URL

/radius?
The search type - this example is radius - there are others like polygon & corridor

key=<YOUR_KEY_HERE>
Replace this with your key here

&origin=1015%20museum%20circle%20jacksonville%20FL
your origin for a radius search can be:
- an address
- an IP address (eg: origin=192.168.0.0.1)
- a Lat,Lng coordinate (eg: origin=40,123,-74.123)

&radius=30
radius in miles

&hostedData=mqap.ntpois%7Cname%20ilike%20?%7Cavis%25
The dataset to search, plus your "filter" search fragment - this is what makes it work how you want:
decoded string, broken down:
&hostedData=mqap.ntpois - this is the table name to search.
Schema is here: http://www.mapquestapi.com/search/ds-ntpois.html#mqap.ntpois
|name ilike ?|avis% - notice the pipe separators. This is the FIELD to filter on, the sql character to use, then a question mark. the question mark is filled in with the value on the other side of the next pipe.
so - &hostedData=mqap.ntpois|name ilike ?|avis%
translates to "select from mqap.ntpois where name ilike 'avis%'

&maxMatches=25
maximum results to return

&ambiguities=ignore
this is only needed if using an address as an origin - this tells it to ignore any ambiguous geocode results and just use the first geocode result as the origin (otherwise, if there are ambiguities, the search will stop)