Make sure the vegetables are relatively dry before starting.
If you need to drain them, reserve the cooking liquid.
To puree the vegetables, put them in a blender or food processor with the olive oil and as much of the cooking liquid (or water or more olive oil) as you need to get the machine going; or run the vegetables through a food mill.
In many cases, you can simply mash the vegetables with a large fork or potato masher, adding the olive oil and cooking liquid as needed to reach the consistency you want.
Taste, then sprinkle with salt and pepper and taste again.
Serve warm, cold, or at room temperature.
It will keep in the fridge for several days.
For the veggies, any cooking method will work: Steam, boil, sauté, grill, or roast — though grilling and roasting concentrate flavors and make the spread more complex.
Just make sure everything is quite tender.