I am hoping to travel and exit the UK on July 29 but my visa is valid only till July 20. I have not begun my journey yet. Is it possible to make this trip and, if so, what do I need to do? Do I apply for a new visa or does it only have to be an extension visa? If it is extension visa what do I have to do differently that applying for a visit visa prior to my travel?
If your visa has expired (or will expire prior to entry), you need to get a new one before arriving. There are no facilities at a UK port to issue entry clearances and you will get removed. In fact, your carrier may not allow you to board.
There is no such thing as an extension to a visitor visa, they are good for a maximum of 6 months and cannot be 'renewed' or extended. You need to make a fresh application using the same way you applied originally.
The new visitor rules are at https://www.gov.uk/government/publications/immigration-rules-appendix-v-visitor-rules note that they have changed since your entry clearance was issued.
If your current visa expires on 20 July, then you will not be able to travel on the 29 July. If you just show up at the airport or train station or whatever else point of exit of your current country, you will simply be denied boarding. Therefore you simply need to act as if you don't have a visa at all - and plan accordingly.
On the positive side, you are still over 6 weeks away from your planned travel date. Which means that you have enough time to apply (and hopefully receive) your new visa.
The first step is to apply for a new visa as soon as possible, providing all relevant information to ensure that your application doesn't get rejected for any obvious reasons. If you have had a visa issued in the past and you have travelled to the UK in the past, you would usually (but not always) have a higher chance of getting your visa application approved.
If it gets rejected, you quite likely won't have enough time to reapply though, although if you move quickly, you may just have enough time. With the new visa rules in effect, the decision usually takes 3 weeks. If at all possible, do not book travel or accommodation until you have your new visa issued.