The Quick Answer

Fourth relates to the number four (e.g., fourth place).

Fourth与数字四有关(比方说，第四位)。

Forth usually means forward or onward.

Forth的意思是向前进或者向前推进。

Forth

The word forth (without u) is an adverb meaning forward or onward (e.g., from this day forth, bring forth, go forth). It can also mean come out into view (e.g., Come forth from the crowd).

forth(没有u)是一个副词，意思是向前进(比方说，从今天起，产生，向前去)。它也可以表示从视野出来(从人群中出来)。

The popular phrase back and forth makes use of the word forth.

短语back and forth(反复地，来回地)就是使用了forth这个单词。

Examples:

Put a cherry on top the first cake, then the second, and so forth.

(and so forth= more of the same)

将樱桃放在第一块蛋糕上，然后放在第二块蛋糕上，依此类推。

(and so forth=更多和这个一样的，以此类推、诸如此类)

I need to be present at the meeting to put my ideas forth.

我需要出席会议来提出我的想法。

Fourth

The word fourth (with u) relates to the number four. It can be a noun (e.g., one fourth, i.e., a quarter), an adjective (e.g., the fourth car) or an adverb (e.g., the new driver came fourth).

Fourth(有u)与数字四相关。它可以是一个名词(比方说，四分之一)，或者是形容词(比方说，第四辆车)或者是副词(比方说，这新车手排名第四)。

很多同学会把这两个词记混是因为他们总觉得这是一个单词的两种写法，因为在英式英语和美式英语中经常会有多一个u或少一个u的拼写差异，但这两个词并不是这样的。其实，你只要记住fourth与four都是数词，而forth是“前进地”的意思就可以啦。