If it's anything like the Steam games I have, then it should be available from your games library. If not, you'll probably have to contact Steam - IIRC, it's the publisher's responsibility to ensure the game comes with a manual.
Note that there is no manual for EU Rome: Gold, but there are manuals for EU Rome (ie the original game) and Vae Victis (the expansion that is included with Gold). The basic manual will give you a rough rundown on everything, but it's very outdated as things get changed with patches over time. The VV manual (available in the FAQ subforum) is really just a list of differences between the original game and the expansion.
If you're still after help, check the Unofficial Strategy Guide, it will give you a few good points to start from.