Learn the sounds used in speaking English, not just the letters that are used to represent the sounds. There are many letters in the English alphabet that are used to represent multiple sounds. For example, the letter "e" has different pronunciations in the words "be" and "bet," and the letters "th" have different pronunciations in the words "bath" and "bathe." You can learn all the sounds of English by reading the chapter on phonetics in most introductory linguistics textbooks or visiting the website provided in the Resources section.
In order to pronounce each sound, you will need to know whether or not to vibrate your vocal chords (known as voicing), how to shape your lips and where to place your tongue (known as place of articulation), and how to manipulate the flow of air during pronunciation (known as manner of articulation). You can find a description of how to produce each sound in an introductory linguistics textbook. By following the link provided in the Resources section, you can hear each sound in English, represented by phonetic symbols, being produced in isolation and in several example words. You can also see both an animated representation of the production of each sound and a video of a native speaker pronouncing the sound.
Practice making these sounds, especially those that are not used in your native language. If possible, practice in front of a mirror, so that you can see your lips and tongue moving into position to create each sound. Seeing yourself pronounce each sound can reinforce what you have learned about how the sounds are made.
Learn how these sounds are pronounced when combined into words and sentences. When people are talking quickly, sounds and words may be pronounced differently than they are in isolation or during careful speech. For example, many English speakers often pronounce "don't you" in fast speaking as "dontchu." Read the phonology chapter of an introductory linguistics textbook or listen carefully to native speakers to learn how the pronunciation changes in casual and quick speech.
Listen carefully to spoken English being used around you or in the media. Listen to the ways the sounds are being pronounced in combination with other sounds, and also pay attention to the rhythm of English--including intonation, stress patterns and pitch fluctuations. Imitate the intonation, stress and pitch patterns that you hear.
Find a conversation partner. Let your partner know about the areas of pronunciation you would like to work on, and ask him to give you feedback and corrections for improvement. A good way to find a free conversation partner is to offer to trade conversation practice in English for conversation practice in your native language, especially if your native language is one that is commonly taught in your area.