Use Wireshark (formerly known as "Ethereal") to eavesdrop on the conversation.
First, make sure that between captures within the same wireshark session, you hit Clear, otherwise filters from one capture (say, an HTTP capture) might interfere with others (say, an ra_svn capture).
Assuming you're cleared, then:
These instructions are specific to the graphical version of Wireshark (version 0.99.6), and don't apply to the command-line version known as "tshark" (which corresponds to "tethereal", from back when Wireshark was called Ethereal).
Alternatively, you may set the neon-debug-mask parameter in your servers configuration file to cause neon's debugging output to appear when you run the svn client. The numeric value of neon-debug-mask is a combination of the NE_DBG_... values in the header file ne_utils.h. For current versions of neon, setting neon-debug-mask to 130 (i.e. NE_DBG_HTTP+NE_DBG_HTTPBODY) will cause the HTTP data to be shown.
You may well want to disable compression when doing a network trace - see the http-compression parameter in the servers configuration file.
Another alternative is to set up a logging proxy between the Subversion client and server. A simple way to do this is to use the socat program. For example, to log communication with an svnserve instance, run the following command:
socat -v TCP4-LISTEN:9630,reuseaddr,fork TCP4:localhost:svn
Then run your svn commands using a URL base of svn://127.0.0.1:9630/; socat will forward the traffic from port 9630 to the normal svnserve port (3690), and will print all traffic in both directions to a standard error, prefixing it with < and > signs to show the direction of the traffic.