Here's my thought process: why would someone talk about something if they don't want input? It seems like a waste of time.
Where's the gap in my thinking? Is there some way I can mentally reframe my thought process so that I 1) Don't immediately try to solve the problem and 2) Don't get annoyed at my significant other for wasting my time.
The remedy they need right now is not a solution. The remedy they need is having someone listen to their situation and empathize.
Bonus: If they really are unable to think of a solution to the underlying problem, after venting about it they will be in a position to better think constructively and even take advice from you.
I mean, if your SO or anyone that you care about is talking with/to you and you could ever possibly think it's a waste of your time no matter what it is that they are saying, then I think you may need to re-evaluate a few things in the new year.
I know where it is you are coming from here, as I also had the same thought process for a long time. Honestly, you just have to find the right kinda people to be around. If you have siblings or parents, you know how it is that everything that you manage to talk about is interesting in some way and how you both know when it's not. Like, during a TV show/movie you really like, even the 'dull' parts are interesting and you are super pumped that they explored the world of the film/show just a bit more. How you want to learn everything there is to know about Star Wars, Marvel, Python 2.7, etc? Even how a Wookie sneezes or Thor shaves?
Yeah, people that you like to be around that much, those are the people to become romantically involved with. Don't become romantically involved with people that 'waste your time' when they tell you about their issues and problems.
Them: My foot is broken
You: Have you considered not walking on it? Have you considered putting a cast on it?
vs
You: That sucks. (mentally: don't ask them to walk on it until it heals)
2) Do you have enough information yet to make a reasonable suggestion? (Smile and nod, shut up)
Them: I don't like my boss and yesterday I ...
You: Why don't you quit?
3) Your suggestion will fix their problem, but what are the consequences of your solution?
Them: I can't walk upstairs to get my medicine (they are on crutches)
You: Let me help you up the stairs (they then need to find you every time they go upstairs. Instead, make sure everything they need is downstairs)
Contrary to GP, I don't think "wait until they ask a direct question" is a perfect strategy; though it's a great strategy compared to shooting your mouth off. Waiting until they ask a direct question is a shortcut to make sure you don't imply that they were too dumb to think of your half-baked solution.