If you do not have a wireless internet connection, Nintendo has hotspots all over. McDonald's a big partner in this, and it's a good option if you are having temporary problems.
Pokemon Diamond and Pearl also supports voice chat. Voice Chat is restricted via Friend Codes. Basically, you cannot talk to people that you randomly meet online: both players must exchange Friend Codes first.
While both the DS and DS Lite have built-in microphones, these might be a bit awkward for regular voice chat. To remedy this, Nintendo is releasing an official DS Headset the week before Diamond and Pearl launch. It retails for about 15 US Dollars.