I think I can help a bit.
First, you need to know the map. There are lots of camping spots, you need to know them to avoid being killed. Also, choosing a good attacking route is important as well as a nice defensive spot.
Second, read the radar and try to guess where your enemies are and what they are thinking. If a place is guarded by 4 people, it is probably not a good idea to go there alone, try to lure some of them out or using your flash grenade wisely.
Third, the basic of FPS games: good aiming. I have been playing CS for 10 years and CS:GO for a while, these two games are basically the same in terms of aiming. Don't panic when you see someone, aim before you fire. NIP is one of the best, or maybe the best, professional CS and CS:GO teams in the world. One of its member -- Friberg made a video to teach people how to aim and to deal with the recoil. I think it is beneficial to you.
https://www.youtube.com/watch?v=eb9nYs4K5e4
If you can spend at least 50 hours on the training map mentioned in the video, you will be a lot better in game: better aiming, better reflexes.
Fourth, play Death-Match mode. If you are new to CS or CS:GO, you get killed often which makes it harder for you to improve your skills because you spend most of your time waiting for the next round. However, you get re-spawned immediately when playing a Death-Match(DM). Playing DM also helps you to know the map faster and forced you to concentrate on the game the whole time, which is really helpful.
Last but not least, get a headset and pay attention to the footstep. Although some experienced players press "shift" when they are moving, most of the players on pub server don't do that. As a result, you can anticipate incoming enemies by listening to the footstep and reading the radar.
I hope this helps. Have fun!
Edit:
1. Aiming for the head.
2. In terms of weapon, it depends on how much $ you have, but try to use rifles all the time. As T, you want to use AK-47 or Galil(if your $ is insufficient), as CT, you want to use M4 or FAMAS(if your $ is insufficient). If you want to play sniping then just use AWP. SG 553 and SCAR-20 are improved in CS:GO. But I highly recommend you practice with your rifles first. Oh, in terms of handgun, USP is a decent one, but I prefer DesertEagle for its instant kill if you headshot someone.
