What is an accent? An accent is the carryover of sounds from the speaker's original language to the second language. When we are infants we literally have the ability to speak any language in the world. We are all born with the necessary speech mechanisms and the ability to learn any language. We end up speaking the language that we do solely by reinforcement. The sounds a baby hears and the speech patterns he is exposed to are the ones that she develops. Soon the baby gains the fine motor skill and control she needs to create sounds herself. The infant will begin by babbling and playing with sounds. Soon she is able to produce simple vowel / consonant combinations which maybe why mama and dada are often their first words, they can make the combination and the big reaction it elicits reinforces their efforts. By 18 months she will be able to produce about 20 words that have meaning and understand around 50 words. Now babies of course have the ultimate immersion experience. In order to obtain any control over their environment they must learn the language and they are surrounded by the language almost 24 hours a day.
Of course the second language learner does not have these advantages. Even if you are now living in an English speaking country, and attending classes to learn English you will still have an opportunity to speak and hear your first language with friends and family, this is especially true in America a county of immigrants where finding a community of People with the same language background is possible.
Another challenge is the anticipation factor. For many years you have heard a speech pattern and there is an expectation of what you will hear when others speak. You are predicting what sounds will come next based on your subconscious knowledge of language. I call this listening with an accent. It is necessary to break through this barrier, to really hear how others are speaking, to actively listen.
To listen is to learn, and I do not mean that in an existential way. I really mean that if you can not hear the way the sounds are produced you can not learn how to produce the sound. Maybe that is why ETS added speaking and listening sections to the TOEFL. The two skills are so closely linked.
Once you can hear the sounds you must add them to your own phonetic library. This means that you have in your mind the knowledge and understanding of how to produce every sound or phoneme in you original language. Now you must add on some sounds that are in the American sound system that is not in your original language sounds system. Record your self reading a brief paragraph. Only 2-3 sentences in English. Then listen to the recording. Write down exactly what you hear on the recording. Not what you meant to say but what you really did say. How is it different from what was written? Did you say th, when it was written or did you say d? I would suggest sticking with the consonants at first because the differences are easier to pinpoint.
If you would like to get help in improving your pronunciation it would be best to go to a speech therapist rather than an ESL teacher. Speech therapists are trained in physiology of the speech mechanisms and musculature. They understand what is involved in producing each sound and are trained to identify and work with articulation problems. Although an accent is not the same as an articulation problem they have similar characteristics. When a client has difficulty articulating specific sounds the speech therapist can hear and see what they are doing differently and describe and show how to do it correctly. When a client has an accent the speech therapist can see what the person is doing differently and show and describe how to make the sound so it more closely approximates the standard.
The most important advice I can give you is to keep practicing. At first it may feel like you are exaggerating when you "speak with an American accent" but I am sure that the native American speakers around you will not even notice. They will certainly be impressed with your great diction!