Four things:
1) Take your time and carefully focus. Increase the magnification on your view screen to max to make it easier to tell when your image is focused on the sky. It doesn't matter what object in the sky you use to focus because if anything is in focus, then everything is in focus (the focus on the moon vs. the focus on a star many light years away is identical.) On a telescope I use a Bahtinov focusing mask.
If your camera does exposure simulation (and I think your Sony camera does) then cranking up the exposure just while you are focusing can help you see the stars. Don't forget to return exposure to a more reasonable setting when you take the shot.
2) Technically, all stars are so very far away that they should expose merely as a single point of light. The reality is that due to the wave nature of light, that's not what really happens. They focus to something called an Airy Disk (named for the astronomer who discovered them). So you'll never really get a star to be truly "pinpoint" -- but you can get close.
3) The atmosphere itself will tend to blur the stars. Astronomers refer to this as "seeing" conditions. I use the analogy of a coin on the bottom of a pool of water. If nobody is making waves on the pool, then you can see the coin quite clearly -- and use binoculars and you might even be able to read the date on the coin. BUT... if someone starts making waves, the coin is going to distort constantly. You might be able to spot the coin, but you'll have an incredibly difficult time trying to read the date. The sky actually does this to us... it causes the stars to wobble and distort by tiny amounts. This is what causes stars to twinkle and also appear to shift colors as they twinkle. The technical name for this is "atmospheric scintillation". But when you see twinkling stars, that means the stars are distorting. Those stars are going to record as even larger blurry spots -- regardless of how good incredibly careful you were when focusing. There are some astronomy websites we use to check the "seeing conditions" but basically if there's either a high or low pressure system within 200 miles of your location and/or if the jet-stream is passing within 200 miles of your location then the seeing conditions are degraded. It can actually be a dead calm on the ground but have horrible seeing in the upper atmosphere -- so you can't just go by whether or not it is windy.
4) Photoshop is your friend. There are a few techniques that imagers use to sharpen the image. One is the "unsharp mask". But note that there's a slider on that tool called "threshold". That's the amount of contrast difference necessary for Photoshop to think this is an area where you'd like to apply sharpening. Increase that just slightly (set it at maybe 1-3) and you'll notice that instead of trying to sharpen the entire image (which generates "noise") it leaves the flat areas of the image alone and only applies sharpening where there's a contrast difference.
Also, there's a tool called the "High Pass Filter" that works well. This tool is a little less straight-forward to use but you can do a search for YouTube video with terms like "astrophotography high-pass filter" and it will probably find several tutorials on how you can use that filter to tighten up the image.
Good luck!