How do I learn opponent ship details?

It has been quite some time since I have played EVE Online, so please view my answer framed with that disclaimer.

Since you mention missions, you might want to make yourself aware of the EVE Survival Guide: http://eve-survival.org/wikka.php?wakka=HomePage. In my mission running days this was an indispensable guide for making my way though missions. It should also be mentioned that there are only a limited number of missions at each mission hub, and you will start to see a lot of repeats over time.

If you are referring to PVP, you can always fit a ship scanner module, but I personally would recommend against it unless flying a specialized ship as a part of a fleet. In most cases when flying solo, the ship scanner will take up valuable CPU and PowerGrid resources that can be used better used for other ship modules. Further, when you consider that a ship scanner will rarely give you an entire list of a ship's modules, the benefit is rarely outpaced by the fitting cost.

Here is how to find out the fitting of the NPC ships you are fighting:

There are some online databases where you can get the configuration of many NPC ships. Note that CCP has stopped publishing this information, so you won't find any new ships. But its still works great for most missions.

• Chruker Inventory Search. Example: Gist Warlord
• EVE Info NPC Ships

There is a new tool for doing exactly this: EVE Fast Fitting Assessment.

EVE Fast Fitting Assessment (FFA) is a Windows desktop application to quickly assess the stats of fittings found on killmails... EVE Fast Fitting Assessment was designed to be useful for EVE players and at the same time also provide insight into a multitude of CREST endpoints for (future) EVE 3rd party developers.

The repo readme contains installation and usage instructions.