Start a Terminal window sussing Applications -> Utilities -> Terminal. In the window, type the following commands one line at a time and paste the output as a reply.
ping 192.168.1.1
ping www.google.com
nslookup www.google.com
dig www.google.com
Here is an exampleofthe commands from my Mac.
nslookup www.google.com
Server: 10.71.30.30
Address: 10.71.30.30#53
Non-authoritative answer:
Name: www.google.com
Address: 64.233.168.103
Name: www.google.com
Address: 64.233.168.105
Name: www.google.com
Address: 64.233.168.99
Name: www.google.com
Address: 64.233.168.147
Name: www.google.com
Address: 64.233.168.106
Name: www.google.com
Address: 64.233.168.104
$ ping www.google.com
PING www.google.com (64.233.168.104): 56 data bytes
64 bytes from 64.233.168.104: icmp_seq=0 ttl=40 time=59.456 ms
64 bytes from 64.233.168.104: icmp_seq=1 ttl=40 time=56.813 ms
64 bytes from 64.233.168.104: icmp_seq=2 ttl=40 time=60.031 ms
64 bytes from 64.233.168.104: icmp_seq=3 ttl=40 time=59.786 ms
64 bytes from 64.233.168.104: icmp_seq=4 ttl=40 time=57.344 ms
64 bytes from 64.233.168.104: icmp_seq=5 ttl=40 time=60.736 ms
64 bytes from 64.233.168.104: icmp_seq=6 ttl=40 time=60.010 ms
^C
--- www.google.com ping statistics ---
7 packets transmitted, 7 packets received, 0.0% packet loss
round-trip min/avg/max/stddev = 56.813/59.168/60.736/1.376 ms
$ dig www.google.com
; <<>> DiG 9.8.3-P1 <<>> www.google.com
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 23986
;; flags: qr rd ra; QUERY: 1, ANSWER: 6, AUTHORITY: 0, ADDITIONAL: 0
;; QUESTION SECTION:
;www.google.com. IN A
;; ANSWER SECTION:
www.google.com. 81 IN A 64.233.168.103
www.google.com. 81 IN A 64.233.168.105
www.google.com. 81 IN A 64.233.168.99
www.google.com. 81 IN A 64.233.168.147
www.google.com. 81 IN A 64.233.168.106
www.google.com. 81 IN A 64.233.168.104
;; Query time: 2 msec
;; SERVER: 10.71.30.30#53(10.71.30.30)
;; WHEN: Mon Jun 1 11:35:49 2015
;; MSG SIZE rcvd: 128