Just connect them together with a straight cable and it should work fine assuming you are not trying to do VLANs or anything fancy.
They don't need IP addresses to work. IP addresses just allow you to control them remotely or to get SNMP data from them. They may very well pick up IP addresses from your DHCP server but it is usually best to use static IPs for things like switches so you can find them easily.
You are creating a minor bottleneck when you connect them this way. The connection between them will be limited to 100 full. If two hosts on #1 want to talk to two hosts on #2 at the exact same time then they will have to share the link so can only get about 50Mb/s each instead of a full 100. So try to get your heavy hitters on the same switch with their main correspondents.
Ron