"Like" and "want" in English are verbs, but in Japanese they are adjectives.

Suki is an adjective meaning "like." Since it belongs to the na-adjective group, its negative form is suki janai and the past form is suki deshita.
It is usually used in the structure, [A] wa [B] ga suki desu.

Watashi wa neko ga suki janai desu.

I don't like cats.

Kodomo no toki, watashi wa neko ga suki deshita.

When I was a child, I liked cats.

Suki shows the taste of the speaker. Therefore, in order to make a statement about a third party, you need to connect it to the pattern, soo desu (Part 3; Chapter 26) showing what the speaker heard or saw, or mitai desu (Part 3; Chapter 25) showing the speaker's guess.

Yamada-san wa sakana ga suki da soo desu.

He said Yamada is fond of fish.

Smith-san wa karaoke ga suki janai mitai desu.

Smith doesn't seem to be fond of Karaoke.

Unlike the English "like," the Japanese suki shows one's unchanging likes and dislikes. Accordingly, it can't be used for selecting something at a restaurant. You should use ii "good, nice" for ordering.

Katoo	:	Nani ga ii desu ka?
Satoo	:	Watashi wa tonkatsu ga ii desu.

Katoo	:	What would you like to eat?
Satoo	:	I'd like to eat pork cutlet.

The usage of ii desu is described in Part 3; Chapter 15. Please refer to it.

Hoshii actually means "to want something," and it doesn't correspond to "want to do something." Since it's an i-adjective, its negative form is hoshikunai. In general, it is used in the structure [A] wa [B] ga hoshii desu, in the same way as suki.

Watashi wa kuruma ga hoshikunai desu.

I don't want a car.

Hoshii means "want to possess something," so you can't use it for ordering at the restaurant.

When you talk about a third party, it should accompany the pattern, soo desu showing what you heard or saw, or the pattern mitai desu showing what you guessed.

The expression to mean "want to do something" is made by adding tai to the verb stem. Since tai is an i-adjective, it has the plain form of -takunai, -takatta and -takunakatta.

Watashi wa eiga o mi-tai desu.

I want to see a movie.

Watashi wa benkyoo o shi-takunai desu.

I don't want to study.

Watashi wa sukii ni iki-takatta desu.

I wanted to go skiing.

It needs to accompany the same patterns as suki and hoshii in order to state the third party's desire.

Nomura-san wa shain-ryokoo ni iki-takunai soo desu.

He said Nomura didn't want to go on the company trip.

-te hoshii, -te morai-tai / -naide hoshii, -naide morai-tai

The expression to mean "I want someone to do something" is made by combining the verb te form + hoshii or morai-tai. The person who is asked to do something is shown by the particle, ni.

Watashi wa kodomo ni motto benkyoo o shite hoshii desu.

I want my child to study more.

Watashi wa Itoo-san ni hon o kaeshite morai-tai desu.

I want Itoo to return my book.

As -te hoshii sounds quite strong, it is often used for stating one's dissatisfaction to someone. -Te morai-tai sounds softer than -te hoshii. It is used for requests.

The expression for such a negative desire as "I want someone not to do" is made by combining the verb nai form + de + hoshii or morai-tai.

Shokuji no toki, tabako o suwanaide hoshii desu.

I want you not to smoke while eating.

Kuruma no mado kara gomi o sutenaide hoshii.

I don't want people to throw trash out the car windows.