The actual mantra is

ॐ गं गणपतये नमः

which when translated with IAST diacriticals is

oṃ gaṃ gaṇapataye namaḥ

Those dots below the letters matter, so when they get lost in non-diacritical translations, it's a bit of a mess.

The "ṃ" isn't really a letter in the original Sanskrit, but rather a nasal marker called an "anusvara". This takes on a nasal sound dependent on the following consonant, which in the "g" case is more like a "n" in the back of your throat. So that's why the mantra without diacriticals is sometimes written "gam" (conveys the wrong idea of what the anusvara is), and sometimes "gan" which is kinda closer but still wrong since it looks like a dental "n" (the only kind of "n" we have in English), when in this case it's actually a gutteral nasal sound instead.

If you want to practice the sound you're looking for, trying saying "gong gong gong gong" repeatedly, but don't do a hard stop between the ng and the subsequent n; just keep the nasal tone going in the spaces. Then replace "gong" with "gahng", and you'll get a feel for what that "gaṃ" should sound like.

The "ṇ" in "gaṇapataye" often gets dropped to a regular English "n" in non-diacritical transliterations, and it's a sad loss IMO. The "ṇ" is a different kind of "n", where the tongue touches the roof of your mouth rather than somewhere close to your teeth (like "n" usually does in English).

Try going "na na na na" a bunch of times ("na na na na Batman!"), but watch where your tongue is hitting, and you'll see it's probably hitting your teeth or somewhere close. Now while doing this, try curling your tongue up so that instead of hitting around your teeth, it taps the top of the roof of your mouth. Then you'll be going "ṇa ṇa ṇa ṇa", and that's the sound you want for the "ṇa" in "gaṇapataye". It's a different feel.

Finally, the "ḥ" in "namaḥ" is another non-letter in Sanskrit, called a "visarga". As mentioned above, it's a breath that takes on an echo of the preceding vowel, so "aḥ" becomes aha, "iḥ" becomes ihi, "uḥ" becomes uhu, etc. But transliterations sometimes lose this, and either write it out with a full vowel, or drop it entirely, neither of which is correct. What you're looking for is somewhere in between, where you fully say "nama" and then give a little bit of a subtle "ha" breath afterwards.

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