As a general rule of thumb you can capitalize adjectives, numerals, prepositions and adverbs, if those are used as a substantive.
There are some exceptions however.
Here is a short overview of them:
The first exception is of course if the Noun (here "der Schüler") is given in the same sentence.
Peter ist der beste Schüler.
as opposed to
Peter ist der Beste.
The second exception is, if it is used in an coolocation such as
durch dick und dünn gehen
The third exception is, if it is used as a superlative and answers the question "how?".
In this example it would be "how cold is it" "the coldest".
Am Südpol ist es am kältesten.
Don't confuse those with those that answer the question "what?".
Wir nehmen nur das Nötigste mit.
Numerals can be written with a capital or not.
Duden says, that you would capitalize it to highlight the Character of the Word as substantive.
Der eine kam, der andere nicht.
Der Eine kam, der Andere nicht.
Also see Duden for the details on "ein/andere".
Numbers are written in lowercase, numerals are spelled with a capital.
die verhängnisvolle Dreizehn
eine Sechs würfeln
as opposed to
Er ist sechzig Jahre alt.
die ersten zehn
For further Details refer to Duden (rule 72 ff).
The above list may not be complete, but should include the most important ones.