The best way to improve a solo q performance is to watch a replay. There are key things which you can see and will help to improve your gameplay over the course of time.
This is not how many skillshots you make its how many skill shots you can dodge efficiently. The more you dodge the more chances you get to make damage. Dodging skill shots damage is a very vital feature for a good player.
2. Total number of wards placed.
There should be a pink ward after your first back when removed should not be missing in the map for more than 3 to 5 minutes. 3 minutes if you are losing and 5 minutes if you are winning. Its free vision and a good cc on the enemy team when they clear the ward. Green wards are subject to the champion and role. After 30 minutes potions and mana pots are useless. So buy greenwards always after 30.
If you are laning against a lane opponent. The highest skill is to know the enemy champions cooldown and damage percentage. It will help you identify when to back and when not too. If your other lanes are losing and you can buy something back immediately. If other lanes are winning then you can dodge and play. So try to see the health after taking damage do a rough calculation and analyse whether you got it or not.
4. wasted time.
How long did you waste your time idle. This is where many people dont understand where the time went. You should not be idle for more than 10 seconds for every minute. 30 seconds is to harass your opponent. 20 seconds is to get cs to yourself or your carries.
5. Watch other people
Always watch others do. They are at the same skill level and understanding the mindset of your entire team is very important. you will find the negatives in their game play which is neat and will help you exploit next time.