If you install from OPM it's a one-click procedure: Check "ZEOSDBO" and click "Install"; confirm the prompt to rebuild the IDE and wait until the IDE restarts (this may take a while...).
If you install from the svn sources, load all packages into the IDE, via "Package" > "Open Package File (*.lpk)". In the package editor of each package, go to "Options" > "Package Options" > "IDE Integration". Those packages which have "Package Type" "Runtime" can be closed because the IDE now already knows where their files are, simply by having opened them (in case of ZEOS, the runtime packages are: ZPlain, ZParseSQL, ZDBC, ZCore, ZComponent). The remaining packages are either pure "DesignTime" or combined "Designtime and runtime" packages - they must be "installed": Click "Use" > "Install". In case of ZEOS, there is only one, ZComponentDesign, confirm to rebuild the IDE and wait until the IDE restarts.
Sometimes rebuilding the IDE chokes on compilation errors, because some compiled units are not up-to-date or are found duplicate at another place. In this case, go to "Tools" > "Configure 'Build Lazarus'" and check "Clean all" and "Switch after building to automatically" in the "Clean up" box. Click "Build".
[P.S.]
I tested this description on Windows and on a VM with Linux Mint (Laz 3.0RC1, ZEOS from svn://svn.code.sf.net/p/zeoslib/code-0/trunk).