The good news: where I work we have a culture in which everyone pitches in when asked. Not your job? Who cares!
The bad news: how do you properly ask for help when no or few special skills are needed? The traditional project management phrasing " I need some resources" is rather demeaning when you're asking for volunteers.*
So around here we ask nicely. We ask for "clueful hands" to help.
Asking for help in a tech shop is tricky. You need people with a specific set of skills (don't ask the Windows desktop support guy for help reconfiguring the Cisco router). However, you're also asking for help, and beggars can't be choosers. So ask for hands (or bodies, but I find that a bit more likely to offend), but be sure to ask for clueful hands. It gives the people who would like to help but don't have the skills a graceful way to back out.
* On a totally unrelated side note, I was at a company once where it slipped out that someone needed "a dev resource" in a meeting with development. We called each other resource for months after that: "Hello, QA resource!" "Hi, dev resource! How was your weekend?"