To say that something is, for example 'bigger' than something else, the item to which it is compared is marked with より 東京は大阪より大きいです。(Tokyo is bigger than Osaka.) You use のほうが to give an answer to questions built with どちら/どっち where two choices are offered 東京と、ロンドンと、どちらが高いですか。(Which is more expensive, Tokyo or London?) 東京のほうがたかいです。(Tokyo is the more expensive.) チョコと、アイスクリームと、どっち好き？(Which do you like more chocolate or ice cream?) チョコのほうが好き。(I like chocolate more.) As for ほど, it's used in negative constructions 英語は日本語ほどむずかしいしくないです。(English isn't as difficult as Japanese.)

Hi, I'll try to explain with simple sentences. I like tea more than coffee. 私はコーヒーより紅茶が好きです。 私はコーヒーより紅茶のほうが好きです。 (You can say in two ways, only with より and with ほうが and より.) I like tea more than coffee, but I like chocolate drink more. 私はコーヒーより紅茶が好きですが、ココアのほうが好きです。 (When you add one more after comparing two things, you can use のほうが.) ほど is used for "not as ... as". I don't like coffee as much as tea. 私は紅茶ほどコーヒーが好きではありません。 If you need more examples, please let me know. I hope this was helpful.

より and の方が are straightforward enough. ほど though, what a nightmare that one is. It has so many different uses. Just thought I should mention ほど can also be used to mean "as (adj.) as" as well. Angelique mentions it can be used in negative constructions, but if we keep the adjective in it's affirmative, we get "as (adj.) as". やぎほどきれい (as pretty as a goat) Good luck with ほど！

よりandのほうがcan be used together in a sentence. AよりBのほうが好きです。(I like B better than A) A より Bのほうがひどいです。(B is worse than A) So you put lesser of two in front of より and stronger one in front of のほうが. ほどhas so many different uses, but in comparison, it is usually used in negative sentence. AはBほど美味しくない。（ A is not as tasty as B) Think, A is not tasty ( as much as B, Bほど). AはBほど悪くない。(A is not as bad as B) A is not bad (as much as B, Bほど) Hope it wasn't too confusing.