I installed memcached for a Drupal 6 site. The status report shows it's properly installed.
How do I check if it's working as expected, and speeding up my site?
You can check the status at /admin/reports/memcache.
Use webpagetest or one of its brethren to see how long it takes for the backed to deliver the HTML. You'll have to compare with and without memcache, warm vs cold cache. There are better analyses you can do, like new relic and blackfire, either requires a web server agent running.