It's been more than forty years since I studied phonetics, but from what I can remember it's true that most, if not all, native speakers of English pronounce the definite article ('the') in different ways depending on whether the next sound is a vowel or a consonant. The actual sounds produced vary from dialect to dialect (and can't be shown accurately without using the symbols of the International Phonetic Alphabet), but again (in very general terms) the tendency is to put a 'y' sound between 'the' and a following vowel. To take Ensiform's example try saying 'the ugly man and the very ugly man'. If you are a native speaker, you should be able to hear a difference between your pronunciation of the two definite articles.
Remember also that spelling is not always a guide to whether a word starts with a vowel. 'Unit', 'ubiquitous' and 'eunuch' do not start with a vowel, but 'hour' and 'honorary' do, despite the way they're spelled.
MK