When trying to alter your accent in order to be better understood, a HUGE part of that change has to do with, not the speech sounds, but the rhythm of speech! This explains why when you hear people from other countries speaking your own language, sometimes the timing sounds different. It might sound choppier or more staccato. It might sound like they're leaving out syllables. This is because they are applying the natural timing of their native language to their second/third/fourth, etc. language. So, how do we change rhythm? It seems like an abstract concept but there are several ways to make this happen.
First lets backup. Generally, languages fall into two types of patterns: we have stress-timed languages or syllable-timed languages. Stress-timed languages use alternating emphasized syllables and reduced, or rushed, syllables. Examples of stress-timed languages include English, German, Arabic, European Portuguese (interestingly contrasted with Brazilian Portuguese which is syllable-timed), Russian, and Thai. So for example, the word "political" in English is pronounced as /puh - LIH - tuh - kuhl/, where the second syllable is produced with it's true vowel, is produced louder and longer, and syllables one, three, and four, are produced more quickly, more softly, and their vowels are reduced to the ol' American English favorite, the schwa (which is just a nerdy word for the sound "uh"). Now that you understand this about English, you'll hear it better! We use the vowel "uh" all the time. It gives our language it's specific rhythm, which can be characterized as a mix of fast and slow syllables.
The other pattern I mentioned is syllable-timed language. Examples of these include Spanish, French, Italian, Brazilian Portuguese, Hindi, Mandarin, and Korean. In syllable-timed languages, equal stress is given to each syllable in a word. Vowels are not reduced to schwas but produced as true vowels. So for example, the word "político" in Spanish would be pronounced as /POH - LEE - TEE - KOH/, where a slight emphasis is placed on the second syllable, but otherwise, each syllable is produced clearly and with longer stress than a "reduced" English syllable.
This concept can be tricky but I've also heard from my students that knowing this makes a big difference in how they not only speak English, but also how they understand English.
Of course, there is more to the rhythm of a language, but this concept is huge! If you're interested in practicing stress-timed English with me, don't hesitate to reach out!