Dropping the G
When a word like going is pronounced more like goin', it's commonly described as "Dropping the G" - but the reality is that it's not! It's actually going to a different sound altogether.
An even bigger mistake is to call this "Lazy Speech." That's a bunch of biased BS.
Working-Class Accents
In my own casual speech, I "drop my G's." I've always done it. That said, when the occasion calls for it, I will put my G's back on. That kind of flexibility is commonly called "Code Switching." I speak a little bit differently depending on the situation.
But when I'm relaxed, I drop my G's.
The reality is that most working-class accents drop their G's in casual speech. This is true of a Chicago accent, it's true of accents of Manchester England, and it's common for many speakers with an Aussie accent. It's most working-class native speakers.
Almost all strong accents of native English speakers follow this same pattern: goin' and doin' and bein'.
Not Really Dropping the G
As I talk about in the video above, you're not really dropping the G sound. You're doing a different sound altogether.
When you say you G in -ING phrases, you're doing the final nasal consonant towards the back of the mouth, with the back of the tongue coming to meet up with the soft palate (also called the velum). This is commonly represented by the phonetic symbol /ŋ/, which looks like a lower-case N and G had a baby.
When you drop the G, it's represented by the phonetic symbol /n/, which is because it's not an N and a G. It's actually a single nasal sound, and it's just happening in a different place in the mouth. /n/ is the tip of the tongue (usually) meeting up with the alveolar ridge or the gum ridge, just above and behind your upper teeth (usually).
I say usually because in reality, you might use the blade of your tongue, and you might do it on the back of your upper teeth instead.
But neither the gum ridge or the teeth are anywhere near the velum/soft palate. And the tip/blade are nowhere near the middle/back of the tongue.
Lazy Speech
This is why I have to call BS on the idea that this is lazy speech. It's actually the same number of sounds, the same number of articulations.
It's not lazy. It requires an equal amount of energy.
So don't be an a-hole and call it Lazy Speech. Or Bad Speech, please. It's not bad if it works, it's understandable, and it fits the occasion.
Most working class accents speak with these kinds of elements of "bad speech." That's why "bad speech" is actually a necessary skill for actors.
Good Speech & Bad Speech
One of the mistakes in actor training is to really focus on elevated speech at the cost of other speech styles. The old school training in Edith Skinner's Good American Speech is thankfully nearing its death. There are good elements to it - her book Speak with Distinction is still the most complete speech drill book that exists. But it's also flawed with some extremely dated pronunciations, and it's full to the brim with bias.
And the actors often lacked flexibility. I tried to get an actor to "put their Rs on" when assisting on casting roles for a Shakespeare festival, and they simply couldn't. Good American Speech was the right way to do Shakespeare. Which is BS. It ain't.
The overcorrection that happened starting somewhere in the 1990s was the mistake of "allowing" an actor to simply speak the way they speak. I've worked with professional actors who were trained from that viewpoint, and they lacked flexibility just as much as the Skinnerian actors did, just in a different way.
There is definitely an issue with many actors not working on their speech in the way they should. The reality of most acting programs is that they don't have enough time to do it in the classroom, either.
There are a lot of causes for the lack of flexibility in an actor's speech. And there's no single right way to do it. But we can try. It's part of why I teach various elements of an accent in a lot of different ways. Hopefully one of them will give you faster access to taking on what the accent demands of you.