Define socially inept
Unable to pick up on body language or subtle cues from people?
Unable to carry on a conversation after it starts?
Unable to approach people?
Unable to initiate conversations?
Saying the wrong things (wrong meaning something the other person doesn’t want to hear, which varies greatly from person to person)?
Self conscious and afraid of looking stupid?
I guess it depends on how you define it. What worked for me was learning social skills and not seeing people as intimidating. What really worked for me was approaching strange women. In order to approach strange women you need to learn to do all of the things listed above and when you can do them reasonably well with strange women doing them with asexual aquantances you work with or go to class with is alot easier. Its like learning to run a six minute mile at 30,000 feet above sea level (where there is less oxygen) then running at sea level with more oxygen (I didn’t take the SATs but if I had I probably would’ve gotten a perfect in the comparison tests).
That advice is completely worthless though because if someone is afraid or unable to commit minor conversation more involved interactions are going to be even harder. Its like telling someone in a wheelchar who wants to learn how to walk ‘learn to run, then walking will be easy’. Its true, but its not really applicable.
So back to the original part. I would suggest reading books on body language and conversation, how to start them and carry them on. There are tons of books on the subject. I would also learn to see other people as alot more vulnerable than they really are. Most people are insecure too, only 10% of women like their bodies, 50% of people say their jobs are high stress, 80% of people say their marriages are unhappy. At the end of the day we all are under the sway of mercurial emotions that we largely cannot control, and understanding that helps. Knowing that other people are afraid of looking stupid, or being weird helps because you know they are not scary objects but individuals with vulnerabilities, and everyone is like that.
Visualization helps too (also known as guided imagery), pretend you are conversing and learn to see signs and pick up on them. Visualization can be just as effective as real life practice.
People watching also helps too, just watch as people interact and talk. Pick up on how they do it.
Learning that other people are self conscious too helps (harken back to the thing above).
At the end of the day, if you do not practice and if you allow yourself to become too vulnerable over what others think to the point where you don’t attempt you’ll probably always be socially inept. Not much you can do about it then sadly. I really have no good advice for how to feel better if people think you’re stupid honestly. “Stop caring” doesn’t work as advice, I have no idea what you can do. I guess it’ll take some serious work mentally to change that if that is partially why you can’t interact well.