I am trying to add a second block of IPs to my EXSi/vSphere 5 setup on a dedicated server. I have so far tried adding a new VMkernel (vmk1) and assigning the gateway and ips to that, but how do I get a virtual machine to actually use them? Any help would be much appreciated.
Firstly you need to do some more learning - not being rude but it's obvious.
Now onto your question, a vSwitch is just that, a layer 2 switch, switches deal with Ethernet, not IP.
The IP address you gave was for the vmkernel (management) process that sits on top of a vSwitch (usually vSwitch0 in fact). You either need a VM port group on that same vSwitch or a new vSwitch with a VM port group defined to expose to VM's vNICs. You then just configure your VM's OS network stack to use IP if you wish, it's got nothing to do the vSwitch.
There is one caveat to this and that's if you're using the IP Pools feature of vApps, then vCenter acts as a form of BOOTP/DHCP server to issue addresses from appropriate IP Pools to VM vNIC in any correctly defined vApp.