It depends on the spatial resolution of your data (e.g. Landsat). With ArcGIS or QGIS you could make a supervised classification. Hope that helps! Cheers

It depends on your interests. In wider view on the interest of a city to become a green city (see for instance European Green Capitals sponsored by European Environmental Agency: you'll find also how define and how compute green open spaces) and how to use local land use to contribute at global change.

In Italy in 1968 some standards were defined for planning. Planning standards represent the maximum ratios between the spaces intended for residential and public spaces reserved for collective activities, educational buildings, health, public parks and parking lots. For green areas, there was two standards, one for neighborhood open space (4,50 sqm/inh) and one for city parks (15.00 sqm/inh). Trees along boulevards and avenues were not computed

In USA there is a software that

“is a state-of-the-art, peer-reviewed software suite from the USDA Forest Service that provides urban forestry analysis and benefits assessment tools. The i-Tree Tools help communities of all sizes to strengthen their urban forest management and advocacy efforts by quantifying the structure of community trees and the environmental services that trees provide. Since the initial release of the i-Tree Tools in August 2006, numerous communities, non-profit organizations, consultants, volunteers and students have used i-Tree to report on individual trees, parcels, neighborhoods, cities, and even entire states. By understanding the local, tangible ecosystem services that trees provide, i-Tree users can link urban forest management activities with environmental quality and community livability. Whether your interest is a single tree or an entire forest, i-Tree provides baseline data that you can use to demonstrate value and set priorities for more effective decision-making. i-Tree Tools are in the public domain and are freely accessible. We invite you to explore this site to learn more about how i-Tree can make a difference in your community. The 2016 version of i-Tree offers several desktop and web-based urban forest assessment applications. i-Tree Eco, i-Tree Hydro, i-Tree Streets and i-Tree Vue are desktop applications. i-Tree Design, i-Tree Canopy and i-Tree Landscape are online assessment tools.”

(https://www.itreetools.org/). This is a very interesting tool, that must be calibrated for every geographical and ecological location.

You could calculate NDVI from Landsat images in ArcGis (https://www.youtube.com/watch?v=GwwXhMKo-yM) and then extract surfaces having 0,3 < NDVI < 0,8. In that way you'll get all the "vegetated surfaces": unfortunately, permeable surfaces and unsealed soils not covered by trees, bushes and shrubs won't be identified as green spaces. 

Another option is to extract green space polygon from openstreetmap (osm) using a GIS software, even though this operation will be successful only if your case study area has been well drafted by osm users. These polygons identify, generally, urban green public spaces, parks, pitches and their perimeters are not dependent on the availability of trees, grass and other vegetated surfaces. 

Once you have built a good green spaces database, you could perform some extra 2D analysis: landscape ecology indicators calculation, for istance, is a good way to describe spatial distribution and configuration of urban green spaces.

If you had a Digital Surface Model and a Digital Terrain Model too, you should perform many other spatial analysis to understand the 3D configuration of urban green areas.

The answer depends on the spatial resolution you want. In case you have cadastral data you can exclude the buildings plot and after that you should proceed to calculation of the NDVI index, or to be more professional, you can proceed supervised classification using remote sensing data 

The answer depends on the extent of the study area but i think you use Enhanced Vegetation Index (EVI) to be able to get the overall vegetation cover in the study area. This index address some of the limitations of the NDVI. The EVI was specifically developed to:

a. be more sensitive to changes in areas having high biomass (a serious shortcoming of NDVI),

b. reduce the influence of atmospheric conditions on vegetation index values, and

c. correct for canopy background signals.

EVI tends to be more sensitive to plant canopy differences like leaf area index (LAI), canopy structure, and plant phenology and stress than does NDVI which generally responds just to the amount of chlorophyll present.

EVI is calculated as:can es

             EVI = G* (NIR-RED)/(NIR+C1*RED-C2*BLUE+L)

where NIR/RED/BLUE are atmospherically-corrected or partially atmosphere corrected (Rayleigh and ozone absorption) surface reflectance's, L is the canopy background adjustment that addresses non-linear, differential NIR and red radiant transfer through a canopy, and C1, C2 are the coefficients of the aerosol resistance term, which uses the blue band to correct for aerosol influences in the red band. The coefficients adopted in the MODIS-EVI algorithm are; L=1, C1 = 6, C2 = 7.5, and G (gain factor) = 2.5.

The output of EVI is a single image layer with values typically from 0.0 to 1.0.

Thanks

You can easily do that with google base maps. But this is very time consuming work. Detect green areas as polygons and calculate their area.

per capita availability of green spaces expressed as Total area of green space (sq.m)/ Total Population of the city.