A photograph that is free to download can still have conditions on reuse. Start with the use you intend: a personal study, a public website, a printed publication and a commercial campaign can require different permissions.
Keep a clear permission record
Read the licence attached to the specific image. Note the creator, source, licence version and any attribution wording. Check whether edits, redistribution and commercial use are allowed. A site-wide label is less useful than terms that clearly apply to the file you plan to use.
Also consider image quality and context. Check the pixel dimensions at the final display size, and avoid using a person’s photograph in a way that implies an endorsement. If the terms are unclear, choose another image or ask the rights holder.