Quick answer
All six orders of Я люблю́ тебя́ are grammatical. The last position carries the new information, so Я люблю́ тебя́ and Тебя́ я люблю́ answer different questions.
What moving a word does
English does this with stress and intonation; Russian does it with position. The end of the sentence is the spotlight.
Where the order is fixed
Prepositions stay in front of their noun (в шко́ле), adjectives in front of theirs (но́вая кни́га), and question words come first (Где метро́?). Everything else can move.
A practical default
As a beginner, use subject – verb – object, like English. It is always correct and always understood. Then start noticing where natives put the new information — usually last.
The test
Ask yourself which word answers the question in the air. That word goes at the end.
Typical mistakes
В шко́ле я иду́ — meaning “I’m going to school”
Я иду́ в шко́лу.
Word order is free, case is not. в шко́ле means “at school”.
Кни́га но́вая чита́ю я.
Я чита́ю но́вую кни́гу.
Free order does not mean any order — the adjective stays with its noun.
Check yourself
Which word carries the emphasis in Кни́гу чита́ет Ма́ша.?