Besides the vowel harmony rules, there are other basic rules that affect the way suffixes are used. A vowel following another is never allowed in Turkish, and there are rules to avoid these situations when they occur as a result of other rules. There are also rules about consonant harmony, that make some consonants change in certain cases.

1. When two vowels come together

In Turkish, two vowels can never come together. So, what do we do when we need to add a suffix that starts with a vowel at the end of a word that ends with a vowel? There are two cases here:

1.1. Dropping a vowel

To say my house, you append the suffix meaning my (-im) to the word meaning house (ev). Simple enough, 'my house' --> evim.

You want to say 'my car'.
Car is araba and the suffix that gives the meaning my is -im. Change the suffix according to vowel harmony rules so that is can be appended to araba (a hard and flat word) and -im becomes -ım.
So, to put it together, my car becomes 'araba-ım = arabaım'. However, two vowels can not come together in Turkish. Trouble...

To avoid this, we drop one of the vowels in this case.
If both of the vowels are in the group "-i, -ı, -u, -ü" than these two vowels have to be the same (look at the vowel harmony rules to understand why). Since the two vowels are the same, it does not matter which one we drop in this case.
However, if one of the vowels is in the group "-i, -ı, -u, -ü" but the other is not (meaning that it is one of "a, e, o, ö") then generally the vowel in the group "-i, -ı, -u, -ü" is dropped. There are some exceptions to this, however, and these exceptions will be noted when necessary.

Applying these rules, 'my car' becomes 'arabam'.

1.2. Adding a fusion consonant in between

You are asked where you are going. You want to say "(to) home". Note that for home, the direction proposition is omitted in English but not in Turkish. Hence, you append the suffix giving the direction meaning (-e) to the word meaning home (ev) and your reply becomes "eve".

However, if you are going to the car and you want to tell this to your friend, life is not that simple for you:

• First, change the suffix -e according to vowel harmony rules according to araba and it becomes -a.
• Now, add this suffix -a at the end of our word araba, and get arabaa.

Two vowels together!! Drop one? Unfortunately, not this time.

In this case, we need to add a fusion consonant between the two vowels. There is not a simple rule to tell why. Sometimes one of the two vowels is dropped, sometimes one fusion consonant is added in between.
However, what you do is consistent for a given suffix. If you are adding the suffix -e to a word that ends with a vowel (like araba), you always add the fusion consonant 'y' in between. Saying 'to the car' then becomes arabaya.
Too much effort spent to say a very simple word? More to come. Let's practice on a few other words:

Coast --> Kıyı    |    To the coast --> Kıyı-e --> Kıyıya

Room --> Oda    |    To the room --> Oda-e --> Odaya

Ship --> Gemi    |    To the ship --> Gemi-e --> Gemiye

This may take some time to get used to, but you can sure do that. But unfortunately, that's not everything. The fusion consonant is not 'y' every time. 'y' is the most common one, so you can put 'y' whenever you don't remember which one to put, chances are high you'll be right. The other consonants that are sometimes used as fusion consonants are 's' and 'n'.

Let's see different cases where these fusion consonants are used:

- The suffix -i

If the suffix -i is used as the -i form of a noun, making it a direct object (like the in English), then the fusion consonant y is used.

araba-i sat -> araba-y-ı sat -> arabayı sat (sell the car)
yazı-i oku -> yazı-y-ı oku -> yazıyı oku (read the text)

If the suffix -i is used as the third person posessive (his-her-its), then the fusion consonant s is used.

araba-i -> araba-s-ı -> arabası (his-her-its car)
para-i -> para-s-ı -> parası (his-her-its money)
kedi-i -> kedi-s-i -> kedisi (his-her-its cat)
* Note that the word for water (su) is an exception for this case, the fusion consonant y is used with the word su (water).

su-i -> su-y-u -> suyu (his-her-its water)

- The suffix -e (direction suffix, adds the meaning of preposition to)

When the direction suffix -e is added to a word that ends with a vowel, the fusion consonant y is added in between.

araba-e -> araba-y-a -> arabaya (to the car)
konu-e -> konu-y-a -> konuya (to the topic)
pencere-e -> pencere-y-e -> pencereye (to the window)

- The suffix -in (gives the genitive meaning, like Andy's)

When the suffix -in is added to a word that ends with a vowel, the fusion consonant n is added in between.

araba-in -> araba-n-ın -> arabanın (of the car, the car's)
konu-in -> konu-n-un -> konunun (of the topic)
pencere-in -> pencere-n-in -> pencerenin (of the window)
ÖbrÇ * Note that the suffix -in is also used with the second person posessive meaning.

If the suffix -in used as second person possessive is added to a word that ends with a vowel, than the letter i of the suffix is dropped. The same is true for the first person possessive suffix, -im, first person plural possessive suffix, -imiz and second person plural possessive suffix, -iniz.

araba-im -> araba-m -> arabam (my car)
kedi-in -> kedi-n -> kedin (your cat)
kapı-imiz -> kapı-mız -> kapımız (our door)
para-iniz -> para-nız -> paranız (your (plural) money)
pencere-im -> pencere-m -> pencerem (my window)

There are also other uses of fusion consonants besides separating two vowels.

- The suffix -le (with, by)

When the suffix -le is added to a word that ends with a vowel, the fusion consonant y is added in between.

araba-le git -> araba-y-la git -> arabayla git (go by car)
kedi-le oyna -> kedi-y-le oyna -> kediyle oyna (play with the cat)
gemi-le gel -> gemi-y-le gel -> gemiyle gel (come by ship)

- The suffix -de (location, like propositions at, in, on) and the suffix -den (proposition from)

When the suffix -de or -den is added to a word as the first suffix, no fusion consonant is used. But when one of -de or -den/ is added to a word that already has a suffix or a series of suffixes that end with a vowel, the fusion consonant n is added in between.

araba-de -> araba-da -> arabada (in the car)
kedi-den -> kediden (from the cat)
araba-si-de -> araba-sı-n-da -> arabasında (in his-her-its car)
kedi-in-ki-den -> kedi-n-in-ki-n-den -> kedininkinden (from the cat's)
gemi-leri-den -> gemi-leri-n-den -> gemilerinden (from their ship)