How to Speak like an American: Linking for smooth sentences

Improving our American English pronunciation often involves a focus on correctly producing sounds at the ends of words.  For example, many accents leave off certain consonants at the ends of words or devoice those sounds, resulting in mispronunciations and misunderstandings.  In general, making sure the ends of your words are clear is a good strategy for being understood.
But what about typical American English?  The truth is, we have patterns of reducing some sounds at the ends of words, and sliding into the next word.  This is called linking.  There are several different types of linking.  To introduce the idea, let's look at a few common sayings and how we link the words in these sayings.

Nice to meet you.  This phrase contains an example of consonant linking.  The t at the end of the word meet runs together with the y in the word you.  We start to say the "t" sound, but instead of releasing the puff of air, we slide into the word you.  Listen the the recording below.  You can hear this sentence with and without linking.  Both are correct, but when the sounds are linked the sentence sounds more typical of American speakers. 

Try these phrases with the same linking pattern:  Eat yogurt.  Bright yellow.  Not yet.

Is he in?  This phrase demonstrates a dropped h.  We leave out the h sound at the beginnings of the word he, and run the z sound from is into the "e" sound of he.  This phrase sounds more like "Izzy in?"  The recording lets you listen to this phrase with and without linking.

Here are some additional phrases with a dropped h.  Is he going?  Call him.  I've seen her.