You can make rapid progress in sounding more natural by understanding a few linguistic features of your target language since these areas pose the greatest barriers to sounding natural.
An example of this is topic marking: explicitly stating the topic of a sentence when it is neither the subject nor the object. For example:
Regarding dessert, I love chocolate cake.
In this sentence “regarding dessert” is a topic marker. Japanese and Korean have special particles for this function. There is no natural way to say this in spoken English. Regarding is bookish and best used in written English; about is also terse and unnatural in this position. Here are some ways we mark topics in English:
[ø] I love chocolate cake.
Context makes it pretty obvious what the topic of most sentences is. Only mark it if you absolutely have to.
I love chocolate cake for dessert.
In cases where context isn’t enough to mark the topic, use a prepositional phrase in the final position of the sentence rather than the beginning.
After looking at the weather, I decided to stay home this weekend.
In more complex sentences, a temporal clause can serve as a topic marker. This can go in either the initial or final position, with before / after being more common in the initial position and because of more common at the end of the sentence.
I looked at the forecast and decided to stay home this weekend.
Sometimes it simply more natural to break the idea into two sentences.
Compare this with Russian:
Насчёт десерта, я люблю шоколадный торт.
Only translate насчёт десерта if the context doesn’t make it obvious.
One of the most obviously unnatural phrases to make it into Russian English is as for me:
Как по мне, лучше отдыхать в горах чем на море.
In almost no cases would as for me be the most idiomatic way to say this in English:
It’s better to relax in the mountains than by the seaside.
I’d rather go to the mountains than the sea.
The mountains are a better place to rest than the sea is.
In each version, the context makes it clear that a personal opinion is being given.
Thus you can make your English such more natural by cutting out phrases that context already makes clear. If you would say насчёт, по поводу or something similar in Russian, you could probably simply skip it altogether in English.