At last, I managed to find an easy way to buy STEEM tokens and if you're interested in buying these in a hurry (i.e. before the price shoots up), I thought the following summary might help.......
The first step is to have a coin/token wallet. However, there is no need to set-up a new wallet as it is already built-in within this STEEMIT social media platform. To see this wallet, click on your profile photo on the top-right-hand of your STEEMIT page.
Now click on the "Sandwich" symbol on the top-right-hand of your STEEMIT page and select "Buy Steem" and complete the form. The most important thing you need is the type of coin you will be depositing here and the Public Key (aka Public Address) which is a mixture of numbers and characters (e.g. "1E9m...."
All you have to do now is transfer either some BITCOINS or ETHER coins from a CRYPTO exchange. I used COINBASE exchange as it also allows you to buy these two coins using the USD from scratch if you don't already own these coins. I found buying with my VISA Credit Card was a faster and more convenient option for me. Although it's possible to buy either STEEM or STEEM POWER tokens, it's probably a good idea to buy STEEM first and then power-up to STEEM POWER later within this platform.
If you're a Newbie to STEEMIT and need a detailed STEP-BY-STEP guide on how to do this, use the following link to an excellent post by 
https://steemit.com/steem/@timcliff/newbie-guide-how-to-buy-steem
I hope this helps but if you know of a better method, please let me know by commenting below.
I'm now working on how to backup these tokens offline for security purposes. If you already know how to do this easily, please add your comments below.