Listen to native speakers, and attempt to emulate the way that certain words come out. Don't think about a word as phonetic as much - think about it as a whole word. And, learn to relate the new language's alphabet to your own. For example, the Hindi alphabet has many more letters than English. Not all of the sounds that you are used to exist in English - we've only got one d, and it's pretty consistent every time you say it. And it's never the d that you say in the back of your mouth, it's always the d that is said just behind your teeth. Same with the t's, and the l's, and the other letters where you have similar sounds but they are said in different places. We just simply don't have them. :) Even once you've gotten most of the letters down, I can tell you that there will probably be letters that you can't say perfectly. Take for example my boyfriend. He is Gujarati, and spoke that as a kid, and is fluent in it with family. However, he learned in an English school, moved to the States, and speaks fluent English with little to no accent. There are two letters in his arsenal that he softly mixes up - v is a hard sound in English, where the teeth touch the lips, and vibrate softly. But he still pronounces it softly like a "w," where the teeth don't touch the lips at all. It's just not a comfortable letter for people that are native speakers of other languages! It's a harsh sound, and isn't easy to replicate unless you grew up with it - just like it is hard for me to use rolled R's, and anusvara. I think the closest English word that I can think of that works like "हूँ" for example, is our word, "whom." Even then, the "m" is a little bit more pronounced than the anusvara is. And I have to remember that when I say "हूँ."
But, anyway, my point is that the easiest way to emulate the sounds of another language is to learn to say them, and if you can think of something that sounds very similar in your language, relate that word back to that sound somehow. Listen to native speakers, and repeat the words as closely as possible. :)
That's how I'm learning Hindi. :)