In your shapefile or axf feature class, you would need a yes/no field for each item. In your form, you would bind one CheckBox control each to each of these fields. There is no way to add multiple items into one field in your dataset without complicated scripting solutions that would essentially sum up to some kind of delimited text string (i.e. Greenery,Garbage Cans,Other).
CheckBox, RadioButton, ComboBox, ListBox controls, in fact all standard form controls can only be bound to one field in your data and can only supply one value to that field.