Correct spelling, explanation: this is the correct form of this ordinal number because the word thirty does not include three in it. If a number ends with three, then its ordinal form suffix is -rd, just like in the ordinal number third. Thirty, therefore, gets the suffix -th which is the most common suffix for ordinal numbers. Thus, 30th is the correct form.

Definition of 30th:
numeral, the ordinal number between 29th and 31st
For my 30th, birthday I’m planning to go on a trip around Europe.
I think coming 30th in the marathon is a huge achievement.

Incorrect spelling, explanation: 30rd is a mistake since suffix -rd is used only to number three or numbers ending with three (for example 33rd, 563rd, 1093rd). Suffix -th is the regular one for ordinal numbers and it is also used for number thirty, therefore 30th is the correct form.

Incorrect spelling

Incorrect spelling