Utilize the proper placement of the mouth, lips and tongue. Proper English is spoken more forward in the mouth than most American accents, and the mouth is held slightly more closed. The tongue is also held further forward, giving the accent a feeling of being frontally pronounced, as opposed to the middle of the mouth used in most American accents.
Resonate sounds in the front of the mouth just behind the gum line. In a general American accent sounds are formed in the middle of the mouth, where the tongue leaves space to form the consonant "R." The proper English is formed slightly forward of this. You can find the proper location by pronouncing a "d" sound, the space where the tongue touches the palette to create the sound is where you should be forming your words.
Use proper English vowels. The two biggest changes in vowel sounds with a proper English accent is the short "o" and the "A". The standard English "A" is a broad open throat vowel and should be pronounced like the "A" in "father" rather than the "a" in "that". The short "o" is used for words such as hot, not and got. These should be pronounced with the "aw" sound from the word "law." In American the "A" in father is often used instead.
Drop the "R" at the ends of words or if it comes before a consonant. The "R" is not pronounced and should be treated like the "b" in "lamb" or "gh" in "daughter".
Observe proper usage of words often mispronounced. The word "been" should always rhyme with the word bean, and never with the word bin as is done in general American accents. "For" is pronounced as "fe" when placed before a consonant or semi-vowel. If "for" comes before a vowel, keep the "fe" sound and add a "R" to the beginning of the next word. "For ever" should become "fe' Rever." On the same vein, the word "to" is pronounced "te" when placed in front of a consonant or semi-vowel and pronounced "too" in front of a vowel.