I installed Elasticsearch on Centos 6.7 using Yum and started pumping documents in (about 450K worth) and now see that my _cluster health is showing yellow.
That's expected with a single node cluster where at least one index is configured to have one or more replicas (which probably is the default in your case).
I want to add another node but want to make sure that I understand the procedure correctly. Do I have to install another instance of Elasticsearch and configure it so that it uses the same cluster name as the first one?
Yes, the cluster name must match.
That is, I will actually have two running instances (nodes) of Elasticsearch?
If so, what if any changes do I need to make to the configuration of the first node? Thanks.
You should set the discovery.zen.ping.unicast.hosts option on each node so that it can locate the other node. With a two-node cluster you should also set the discovery.zen.minimum_master_nodes option to 2 to avoid split brain situations. Note that to get a cluster that survives even with one node down you need three nodes, not two.
Depending on what your current configuration is you may also need to adjust the network.host setting so that Elasticsearch binds to non-loopback interfaces.