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You can check this in many ways. large plastic sheet set down on the floor and sealed tight with duct tape works well. leave it there for a week or so. If you begin to see moisture collect under the plastic you need to take measures to correct this issue before doing anything else. Try this
If you see any white powder anywhere on the floor cover that area also. This white powder is the result of moisture reacting to the salts in the cement and depositing the salts on the surface as it evaporates away.
If your floor passes the moisture test, then stain is normally the best way to go if you want a long lasting color. Epoxy systems also work well, bit harder to use and Ideally should be professionally done if you really want it to last.
The bottom line here is be sure you have no moisture and if so correct this first. Then what ever you decide to use, you must follow the directions very carefully on the product that you choose if you decide to do this yourself. And most important that you properly prepare the surface by cleaning it really well. As with any finish the end results are always the byproduct of the prep. Which of course is the worse part of the job.