You can use traceroute to determine the network path packets follow from
your machine to some host server. For instance, if I want to know path
between my laptop (connected to airport wifi) and my website
joshbranchaud.com, I can run the following
command:
$ traceroute joshbranchaud.com
traceroute to joshbranchaud.com (198.74.60.157), 64 hops max, 52 byte packets
1 hotspot.boingohotspot.net (192.168.144.1) 1.209 ms 1.427 ms 1.080 ms
2 192.168.13.1 (192.168.13.1) 5.272 ms 3.545 ms 6.231 ms
3 10.106.144.1 (10.106.144.1) 13.671 ms 15.311 ms 12.895 ms
4 68.13.10.184 (68.13.10.184) 14.789 ms 12.980 ms 13.628 ms
5 68.13.8.221 (68.13.8.221) 19.922 ms 12.611 ms 17.853 ms
6 nyrkbprj01-ae3.0.rd.ny.cox.net (68.1.5.157) 48.917 ms 56.641 ms 51.771 ms
7 eqix.e-2-3.tbr2.ewr.nac.net (198.32.118.157) 62.977 ms 52.970 ms 48.667 ms
8 0.e1-2.tbr2.mmu.nac.net (209.123.10.114) 66.253 ms 57.311 ms 52.242 ms
9 207.99.53.46 (207.99.53.46) 57.478 ms 53.443 ms 54.510 ms
10 joshbranchaud.com (198.74.60.157) 59.853 ms 56.375 ms 55.393 ms
See man traceroute for more details.