I'm assuming you have already built your entire model in the simulation program, and just want to cherry pick the zone you want.

It's not very practical to delete all the rest of the zones, as many objects are linked in E+ and having left-overs not linked to the objects E+ is expecting will lead to a crash. Therefore, the easiest way, if simulation time isn't too bad, is to run the entire model and then isolate the output.

I can't give you an OpenStudio specific solution as I'm not familiar with it, but this should get you started.

E+ has two ways of reporting:

1) The easiest is to select one of the predefined Output:Table:SummaryReports. The one you will be most interested in are ZoneCoolingSummaryMonthly and ZoneHeatingSummaryMonthly.

ZoneComponentLoadSummary as @Amir Roth mentions, is also very helpful to understand where peak heating and cooling loads are coming from by breaking it in various components (peak loads, not energy used)

Check out the Input/output reference, section "Output:Table:SummaryReports" and especially the subsection "Predefined Monthly Summary Reports" (here online)

Example

Output:Table:SummaryReports,
AllSummary,              !- Report 1 Name
ZoneCoolingSummaryMonthly,  !- Report 2 Name
ZoneHeatingSummaryMonthly;  !- Report 3 Name
ZoneComponentLoadSummary,!- Report 4 Name

2) You could also ask for specific variables (HVAC,Sum,Zone Air System Sensible Heating Energy [J] and HVAC,Sum,Zone Air System Sensible Cooling Energy [J]) using either Output:Variable, or use the convenient Output:Table:Monthly object if that makes sense for you.

Example:

Output:Table:Monthly,
Zone Heating and cooling loads,  !- Name
0,                       !- Digits After Decimal
Zone Air System Sensible Heating Energy ,  !- Variable or Meter 1 Name
SumOrAverage,            !- Aggregation Type for Variable or Meter 1
Zone Air System Sensible Cooling Energy ,  !- Variable or Meter 2 Name
SumOrAverage;            !- Aggregation Type for Variable or Meter 2