I recently had a customer reach out because she was concerned about putting her silicone travel lids on correctly. I've been using these travel mugs myself for years, and I know it's kind of tricky to get the hang of putting the lid on.
I recommend resting the lid centrally onto the top of the mug, and then pressing down gently and evenly across the entire lid with the full palm of your hand. If you do this gently enough, it should simply "snap" into place when the lid stretches just over the lip of the mug. It's very easy to press too hard when you're getting used to this technique, and having the lid slide down on one side past the lip, but that can be fixed by gently pulling back up on that side.
I think it's a lot easier to understand with a demonstration, so I recommend watching the video above.