Luckily for us, linguists have spent a long time working on this issue already and there is a very comprehensive set of symbols that can be used to transcribe the sounds of English - or any other language for that matter. If you have a bilingual dictionary (or even a good monolingual English dictionary) you will find a list of these phonemic symbols and examples of the sounds they represent. In most cases, these symbols will be an adaptation of the International Phonetic Alphabet (IPA).
It is worth taking a moment to consider the difference between a phonetic transcription and a phonemic transcription. When using phonetic transcript, we represent the exact sounds of the word and use allophones. A phonemic transcript, on the other hand, only shows the pronunciation in terms of the phonemes.
Many of the symbols in the IPA (and the phonemic chart) are similar to those in the Latin alphabet, particularly with the consonants. For example, the initial phoneme in the word pen is transcribed as /p/ and the final phoneme in yes is transcribed as /s/. However, there are some symbols for phonemes that are not represented by one single letter in English. To become more familiar with the different phonemic symbols of English, I really recommend you look at the British Council's interactive phonemic chart. Try playing around with it until you're familiar with the symbols and the sounds they represent.
As you have maybe noticed, all the phonemic symbols have been written between forward slashes (//). This shows us that they are phonemes and not allophones (allophones are written between square brackets (). If you want to write phonemic transcripts using Word, selecte the font Lucinda Sans Unicode - and use Insert Symbols to find the complete range of phonemic symbols.
Perhaps the biggest challenge when we start using phonemic symbols (besides trying to draw the more unusual ones) is to stop thinking about spelling and start thinking about sounds. Taking the word jam as an example, it would be tempting to suggest that the first phoneme is /j/, although this is wrong. Don't worry though, with a little practice you'll soon get the hang of it.
If you want some practice, try to decide what phoneme these words begin with: