You would use the vb database manager to run the query and gather the info like so....
PHP Code:
$fields=$vbulletin->db->query_read("select fieldNumber from ".TABLE_PREFIX."userfield order by rand() limit 10");
Then loop through the data and structure it however you want using the $vbulletin->db->fetch_array() function...
ex....
PHP Code:
while($field = $vbulletin->db->fetch_array($fields)){
///Process data...
}
You would want to put this in a plugin that hooks the proper location, more then likely the forumhome_start hook location since you want to display it on the forumhome template... Usually format and place all the data into a variable and then edit the template of which your plugin is hooking and add that variable. VB also has Template hooks where you can add data to pre-defined variables that will get displayed in the templates without ever editing a template.