Without seeing your technical developer's code, I could only guess why he/she might be having trouble, and php.net is the authoritative guide on "sample code for how to session will work" on any server.
Between the phpinfo() output your developer has, and the php.net manual, there are no special "tricks" to getting session code to work on DreamHost.
There are some significant differences between the two environments in which your developer is working, and his/her code needs to take this into consideration:
1) DreamHost is running PHP-CGI, while the other server is running mod_php
2) DreamHost is running PHP 5.2.3, while the other server is running PHP 4.4.4
3) Dreamhost is running with register_globals disabled, while the other server is running with them enabled.
4) DreamHost has allow_call_time_pass_reference off, while the other has it on (same for allow-url-fopen)
... and probably others. Your developer needs to take these issues under consideration with his code (though not all of these differences are relevant to sessions handling).
One thing you might consider trying, if you do not object to running code under PHP4, is to change your DreamHost domain to use PHP4 instead of PHP 5 (you can do that in the control panel). That will eliminate some of the differences in the environments (to the detriment of security on the DreamHost side ) and, depending upon your developer's code,may help him get his/her code working.
That said, you are far better off, as is your developer, in getting his code to work in the more secure DreamHost environment using PHP5, IMHO.
Edited to provide additional info: Your developer can good examples of robust session handling code in the open source of several of the applications DreamHost offers as "one-click" installs. Particularly, I think that Joomla! offers some fine examples!
At a "simpler" level, here are two php scripts that demonstrate handling sessions in the DreamHost PHP 5.2.3 environment:
First, storing to session...
Next, reading from session...