Since you haven't mentioned which specific mods you're having problems with I can only give you general advice here, but have you tried:
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Verifying your game files in Steam - just in case the problem's with your base game files rather than with the mod in question.
- Running only one mod (i.e. not the ingame editor, or any other mod, at the same time) - it is possible for mods to conflict with each other such that they will not work at the same time, even if each one works individually.
- Trying a different mod. I know you say you have this problem with any mod, but I doubt you've tried every single mod on the workshop. You may have just been unlucky and picked ten buggy and unreliable mods in a row.
- Checking that you have/don't have any DLC that the mod in question requires you to have/not have. (This should be mentioned in the mod's description) - If the mod requires Brave New World, for example, and you don't have Brave New World, then it will not work.
- Checking that the mod in question is, in fact, supposed to add new researchable/buildable units. (Again, this should be mentioned in the mod's description) - If you've misunderstood what the mod is supposed to do then it may actually be working perfectly.
- Talking to the person who created the mod in question, by posting on the Steam Workshop or Civfanatics thread you downloaded it from. - This is the person who will be best able to solve problems you're having with this specific mod, which may or may not be the same problem that is stopping a different specific mod from working for you.
Be as thorough and specific as you can in describing the problem, i.e. which parts of the mod's content do appear, which don't, screenshots showing the problem, any error messages that appear in log files, which expansion packs and DLC you have, whether you're on PC or Mac, and anything else you think may be relevant.