When you speak you must pay attention to saying utterances fluently, smoothly, with no gaps or hesitations in the middle. In English words are not separated from each other: the end of one word flows straight on to the beginning of the next.
One of the difficulties which foreign learners often face is connected with a vowel at the beginning of words, especially if it begins a stressed syllable. For example, /*bIg *xpl/. English speakers glide smoothly from the final sound of the word to the initial vowel of the following word with no break, no hesitation. When the final sound of the word before is a consonant, it will help if you imagine that it belongs to the following word (e.g. /*bI *gxpl/).
If the final sound of the word before is a vowel there are various ways of connecting two words together. There are several linking sounds that help us to do it. If the word ends in /J/, /I/, /aI/, /eI/, /OI/ we can use a little /j/-sound as the link. It is very gentle. We distinguish between my ears and my years (/maI *jIqz/ and /maI *jIqz/), where /jIqz/ has a longer and stronger /j/ than the short and gentle glide before /Iqz/.
Similarly, after /H/and diphthongs /qV, aV/ we can use linking /w/-sound. Again we distinguish between two-eyed and too wide (/*tH *waId/ and /*tH *waId/): /w/ in /waId/ is longer and stronger than the linking sound /w/.
Some vowels can be linked to a following vowel by /r/. We can speak about two kinds of /r/-sound: linking /r/ and intrusive /r/. RP has a word-final /r/ as a linking form when the following word begins with a vowel. So, linking /r/ exists in cases where there is a letter ‘r’ in spelling at the end of words (far off /fRr Pf/, four apples /fLr xplz/). By analogy, /r/ can be used to link words together even if there is no ‘r’ in spelling. This kind of /r/ is called intrusive (Russia and China /rASqr qnd CaInq/, idea of /aIdIqr qv/). Its usage is greatly disapproved of by native speakers, so you’d better avoid using it in speech.
When we connect other vowels to a following vowel without linking sounds, we just glide smoothly from one to the other with no interruption of the voice.