spec maps are a somewhat complicated subject. and one many artists either overlook or dont understand how to use effectively.
first general process quick.
ill take the diffuse and do some levels or brightness and contrast. trying to increase contrasts and darken somewhat. how much depends on your game engine and the material your emulating. it takes some testing to get that right. then ill multiply the ambient occlusion image on top of that. then sometimes ill add in some noise or tiling photo texture to add some small variation and detail. i'll test the map by constantly re-importing it with different changes untill ive gotten the look i want. once and done just doesn't cut it. That's the quick and dirty approach.
Sometimes ill also multiply some wear and tear, streaks as those things reduce the specular on objects.
Commonly there are some mistakes artists make with specular.
1. Not enough of it. that's mostly because they don't test their work enough and don't have any reference pictures for the material they are emulating.
2. They take some kind of purist attitude about it. like specular isn't real so you shouldn't even use it. its not about ideology, Its about looking good.
3. Its actually bad to have your specular detail at the same frequency as your diffuse map. What does that mean. It means that the detail scale in the spec map should be offset from the diffuse otherwise the forms won't read right. Specular and diffuse can cancel each other out if they are the same detail scale or size. Technically you should approach specular maps as a new map instead of copying the diffuse over with some adjustments. I recommend some experiments with that to see what I mean.
Get reference, and test, test, test, in your engine. It also wouldn't hurt to read up on the subject and start to really understand it. you may learn some surprising things. Like, skin returns a white specular, not red, or pink, or anything else. The specular component of skin is always white. The sub surface, or transmission light is usually pink orange or red.
Hope that helps….