How can I translate the sentence "in science I trust"? I tried using Google Translate, but it was unhelpful.
Salve. I will begin with the verb. I think the best option here would be fīdere, which takes either the dative or the ablative. The verb "I trust" is first person, singular, present, indicative, active. This would translate as fīdō. A common word for trust in is cōnfīdō. You might want to use this form as, I believe, it is more attested. Your phrase, however, reminds me of the U.S. motto "In God We Trust," so you may want to translate it as cōnfīdimus (we trust) instead.
Now for the object, "science." Scientia is the first word that comes to mind. It is also the word used in Vicipaedia, Latin Wikipedia. Scientia is, however, more conceptual, having meanings such as "art," "knowledge," and "skill" (Elementary Lewis). You might, therefore, want something slightly more specific: Vicipaedia also gives "scientia rationalis" (rational science). Another option could even be philosophia because, for much of history, science and philosophy were inseparable. Although, I think scientia rationalis is probably a good choice here.
To put it together, you get scientiae rationalī cōnfīdo.
There are two main ways this kind of idea is expressed in Latin. One particular to epigrams and mottoes uses the noun FIDES or verb FIDO and the other is the verb CREDO. To express the idea of "trusting in X" as we would say in English, the Romans would generally use the verb credo. So, there are three basic options:
Scientiae fides (In science there is trust) Fide scientiae (Trust in science) Crede scientiae (Trust in science)
Notice how in all three mottoes, the dative is used. This is because when you are giving something (like trust) to someone, you use the dative. For example, there is a famous Latin motto "Fronti nulla fides" which means "In appearances there is no trust". Notice how Fronti is in the Dative case. In English we think of putting trust IN something, but to a Roman it is giving trust TO something like a gift.
There are some other, less standard ways to express the idea which use the word hope (spes):
In scientia spero Spes scientiae. (Trust to science.) Scientiae fido. (I trust in science)
In modern forms of Latin where you would, for example, trust in God, typically the word spero (hope) is used. So we have "In Deo spero" (In God I trust).
Here are some related mottoes:
Mus non uni fidet ultro. -- Plautus (The mouse does not trust in one hole only.) Nimium ne crede colori. -- Virgil (Trust little in good looks.) Oculis magis habenda fides quam auribus. (old Latin proverb) Spes sibi quisque. -- Virgil (Let everyone trust in themselves.) Virtuti non armis fido. -- Motto of the Earl of Wilton (I trust in virtue, not weapons.)
If you are using this as a motto, probably the best choice is analogous to Earl of Wilton's motto, so you would say "Scientiae fido". This form is short and follows the basic heraldic pattern found in other mottoes.