I think there are many ways to use two verbs in a sentence.
Anyway, your example would be translated into like this:
#1:彼女に会うために学校に行きます。
#2:彼女に会いに学校に行きます。
The case of writing a purpose to do something:
in order to do
=>
#1 verb(dictionary form) + ために(or ため)
or
#2 verb(stem of マスform) + に
#1 食べ物を買うためにスーパーに行きます。
#2 食べ物を買いにスーパーに行きます。
These have the same meaning.
However, as Jaida-san wrote, #2 phrase can only be used with movement verbs like 行く、来る、戻る、帰る.
#1 phrase can always be used.
So may be it's easier for you to start with #1 phrase.
And if you learn a Verb stem of マスform, you can make another way to use two verbs like Garrett-san wrote.
I finished reading a book.
本を読み終わりました。
I started learning Japanese.
日本語を勉強し始めました。
These are:
verb (stem of マスform) + verb(meaning to start, finish)
読み+終わる=読み終わる
勉強し+始める=勉強し始める
I hope this helps you!