Trapping happens at output when you print separations. There are options in the print dialog to use InDesign's built-in trapping or a RIP's trapping. If you use ID's then the trapping parameters are set in the Trapping panel.
Colors other than default black don't overprint by default, so if you are looking for an overprint effect you'll have to select an object and set its fill or stroke to overprint via the Attributes panel.
You shouldn't have to add your own traps. That should be handled by the RIP. If you for some strange reason need to add traps to objects (something like printing film or separations for cut vinyl directly from InDesign) you'd want to know what the traps need to be and set them in trap presets, found under Window > Output > Trap Presets.
Odds are you aren't going to know what you are doing in there and will want to ask what the heck they want. This is a good opportunity to ask why the RIP isn't doing its own trapping and separations like RIPs have been doing for years.
Also go in Window > Output > Attributes. Most likely you'll just want to set some selected objects to overprint. Make sure the document looks correct in Overprint Preivew (View > Overprint Preview).
If I hadn't mentioned it yet, trapping is something you shouldn't ever have to do. You can also do this in Acrobat to some degree and be just as well off.