In connected speech, the pronunciation of a word will change depending on the words around it. Changes in pronunciation within and across word boundaries include changes to individual sounds and new sounds being inserted. Learners have to become aware of these changes in order to understand authentic speech, and to help their pronunciation.

Example
Intrusion: If the words 'go' and 'up' are said together, there is a new /w/ sound between the two words.
Elision: The disappearance of a sound in connected speech; chris(t)mas, int(e)rest.
Linking: We tend to link final consonants and initial vowels across word boundaries.
Weak forms: In connected speech, many words are pronounced in a weak form.

In the classroom
Intensive listening activities can help raise awareness of the features of connected speech, as can teaching phonemic symbols to illustrate these features. Modelling and drilling contextualised language can help learners to approximate connected speech.

Further links:

https://www.teachingenglish.org.uk/article/connected-speech-2

https://www.teachingenglish.org.uk/article/helping-teens-listen