If you want to avoid what occurred in this video. Read on!
Step 1: Don't Get Lazy
Like show in the video you want to go mining and you start to dig straight down because its quicker that way. You start finding all kinds of ores and its going quite well. But then suddenly you fall into lava right under the block you just mined! There is not escape it just GAME OVER!!!
Step 2: Possible Solution #1
When you start to mine dig a staircase that you can walk down. This is a very efficient way for mining and it is easy to avoid falling in lava.
Step 3: Possible Solution #2 *Advance*
The second possible solution is to dig 2x1 hole while holding down shift. When you start mining dig the opposite block. This is a good solution because it reduces the chance of falling in lava but it helps you reach bedrock quicker.