Archie, the short game can be the most frustrating part of the game but there are a few basic things you can do to improve it relatively quickly.
Chipping: Most players weak in this area are weak because they don't understand that you still strike THRU the ball. You will find chilli-dippers or may be one yourself because they/you are so afraid of hitting the ball past the hole or maybe skull it across the green. These types tend to stop at impact but what this does is usually is raise or lower the hands from where they would have contacted the ball had they swung thru impact.
Even those players who avoid chunking the ball but still have troubles often have trouble because they want to HELP the ball instead of allowing the club do the work for them. Provided you choose the correct iron and TRUST your ability you would be amazed at how simple chipping can be.
Putting: One tip that never fails to improve almost immediately is seeing the ball pass thru you peripheral.
There are other tips to putting but the one I just gave you will make a serious impact immediately because it is instant reassurance that you kept you head still.