You can use dig or nslookup, say your (or your provider's if you don't run your own) nameserver is ns1.example.com.
nslookup - ns1.example.com
At prompt type:
If it resolves to what you expected then it works. It should give you something like:
It may still take a while to propagate to the rest of the internet, that's out of your control.
You should see something like:
;; ANSWER SECTION:
example.com. 172800 IN A 184.108.40.206
Just using ping may give you an idea, but only when it has propagated (cached by remote nameservers may be a better way to describe it) and your local dns cache may need to be flushed. Although in your case this does not apply because this is a new record. In that case it should be available immediately. The above way is more precise in giving you an idea as opposed to just pinging it.
If you use windows then the commands and syntax may differ slightly, but are pretty similar.