The best thing a non-miner can do to support the network and signal their support for SegWit would be to run Bitcoin Core 0.13.1.  You can see that currently 30% of the nodes on the network are running 0.13.1.
https://bitnodes.21.co/nodes/

You could also find a site that offers a voting mechanism to make your opinion heard.  Here's one for example: https://vote.bitcoin.com/arguments/segregated-witness-is-a-good-short-term-approach-to-scaling-bitcoin-capacity

Currently, 52 of the last 300 blocks (17%) signaled SegWit support, and 32 of the last 142 blocks (23%).  You can monitor progress here:
https://data.bitcoinity.org/bitcoin/block_version/7d?c=block_version&t=a