There are many freeware applications suited for this task, some can even run on your phone.
Check out this list by Network World:
Furthermore, a handy Android app is "WiFi Analyzer":
The above app will show you graphical representations of shared channel overlap, as well as other stats like signal strength, etc. - very handy for mapping signal strengths.
In terms of technique for your survey, a solid course of action would be:
1: Submit your Plan of Action for approval: Since this is a .gov facility, you'll likely need to comply with their in-house Information Assurance & Change Control guidelines - this will entail putting together your plan-of-action (things you will do) and if need be, a back-out plan (how you'll restore service(s) if something goes wrong). Note that this plan of action should also include the software you'll be running to scan WiFi signals, so that they understand you're not doing something nefarious like sniffing without permission.
2: Obtain a floor-plan, and note the zones which your wifi will be required to cover: Mark these zones with unique identifiers like "Zone A", which will allow you to easily name and track your WiFi mesh nodes ie: "GOV-WAP-A2" - this will facilitate ease of maintenance in case someone else is called in to work on your setup.
3: Using your above zones, map the signal strengths of each existing WiFi signal in the areas you're supposed to cover - choose the WiFi channel which is least-used in that zone to be the channel used by that AP (or multiple APs, depending on your type of coverage / service-set). Record this zone data as part of your survey and note it in your design document.
4: After your APs are configured with the proper channels / etc you desire, do a second site-survey and note signal strengths of all APs in each zone as needed, and do a full walk-thru with a constant "ping" running, to watch WiFi handoff between APs, and adjust accordingly. Note all signal strengths in your final report, so that they can see what you've delivered.
NOTE: With .gov projects, documentation is a huge part - depending on the agency, you may be held accountable in the future if your work is not up-to-spec with what they expect.