In practice, if you already have an SSL server, just add the "spdy" to the listen line like "listen 443 ssl spdy;", restart and you are done[1].
Then making it proxy request is just one location definition with "proxy_pass"[2].
[1]: http://nginx.org/en/docs/http/ngx_http_spdy_module.html
chadaustin already mentioned nginx, which seems to be the most popular choice.
This is alos one of the examples for H2O:
… and Apache Traffic Server just shipped support in v5.3.0, which might be of interest if you want to setup a generic front-end layer for a ton of backend services:
https://cwiki.apache.org/confluence/display/TS/What%27s+New+...
One thing I haven't looked into is whether any of these will try to use server push for content which has is referenced by <link rel=preload> in an HTML page. That could be very useful for render-blocking CSS/JS.