Grammatical gender in French is pretty much arbitrary. There's not much to understand. Sorry.

The usual tip when learning a language with (mostly) arbitrary grammatical gender like French or German is to always learn the article with the noun. When you learn the word for car, learn “la voiture” or “une voiture”. I think I the definite article is taught more often, but it has a downside of hiding the gender if the word starts with a vowel sound: better learn “un arbre” than “l'arbre”. Make sure you understand the pronunciation of the indefinite article though: “une arme” and “un arbre” only differ by the vowel sound (and the noun itself), since the E in une is silent and the N in un is sounded due to the liaison with the following vowel.

Nouns that specifically designate male people (or animals) are masculine. Ditto for females and feminine nouns. (There are a few exceptions with professions that are traditionally gendered.) These nouns usually come in pairs, e.g. “père/mère” (father/mother), “acteur/actrice” (actor/actress), “chat/chatte” (male/female cat). With such pairs, apart from a few common words, the male and female forms differ only by a suffix, the female suffix always ends with -e, and the suffixes mostly follow the same patterns as for adjectives.

Apart from that, you can't rely on the meaning of the word. Even if two nouns are synonyms, that doesn't make it more likely that they have the same gender.

You can sometimes rely on the ending of the word. Many word endings are strongly gendered. You may want to learn the most common ones, but I'm not convinced of the effectiveness of this approach: that's one more arbitrary classification to learn, and most classes have exceptions that you'd need to learn anyway.

I think (but I have no data or personal experience to support it) that it would be more effective to learn nouns on an individual basis. Once you know a critical mass of nouns, you can start looking for patterns: if you're unsure about the gender of a noun, try to think of a few words with the same ending; if they all have the same gender then chances are that the noun you're wondering about has the same gender.

What works better than endings is suffixes. Many suffixes have a single gender. If a word is built from a stem and a suffix, then once you recognize the suffix, you know the gender of the noun. For example, -tion is exclusively a feminine suffix, so any word built with that suffix is feminine, e.g. you don't need to learn words like vasoconstriction or mobilisation to know their gender. But there are a couple of words that just happen to end with those letters (e.g. cation is not ca- + -tion, gestion is not ges- + -tion), and they can be of either gender. (In this case, recognizing the suffix also tells you the pronunciation of the word: the suffix -tion is pronounced [sjɔ̃], but the letters “tion” are otherwise pronounced [tjɔ̃].)

Grammatical gender in French is pretty much arbitrary. There's not much to understand. Sorry.

The usual tip when learning a language with (mostly) arbitrary grammatical gender like French or German is to always learn the article with the noun. When you learn the word for car, learn “la voiture” or “une voiture”. I think I the definite article is taught more often, but it has a downside of hiding the gender if the word starts with a vowel sound: better learn “un arbre” than “l'arbre”. Make sure you understand the pronunciation of the indefinite article though: “une arme” and “un arbre” only differ by the vowel sound (and the noun itself), since the E in une is silent and the N in un is sounded due to the liaison with the following vowel.

Nouns that specifically designate male people (or animals) are masculine. Ditto for females and feminine nouns. (There are a few exceptions with professions that are traditionally gendered.) These nouns usually come in pairs, e.g. “père/mère” (father/mother), “acteur/actrice” (actor/actress), “chat/chatte” (male/female cat). With such pairs, apart from a few common words, the male and female forms differ only by a suffix, the female suffix always ends with -e, and the suffixes mostly follow the same patterns as for adjectives.

Apart from that, you can't rely on the meaning of the word. Even if two nouns are synonyms, that doesn't make it more likely that they have the same gender.

You can sometimes rely on the ending of the word. Many word endings are strongly gendered. You may want to learn the most common ones, but I'm not convinced of the effectiveness of this approach: that's one more arbitrary classification to learn, and most classes have exceptions that you'd need to learn anyway.

I think (but I have no data or personal experience to support it) that it would be more effective to learn nouns on an individual basis. Once you know a critical mass of nouns, you can start looking for patterns: if you're unsure about the gender of a noun, try to think of a few words with the same ending; if they all have the same gender then chances are that the noun you're wondering about has the same gender.

What works better than endings is suffixes. Many suffixes have a single gender. If a word is built from a stem and a suffix, then once you recognize the suffix, you know the gender of the noun. For example, -tion is exclusively a feminine suffix, so any word built with that suffix is feminine, e.g. you don't need to learn words like vasoconstriction or mobilisation to know their gender. But there are a couple of words that just happen to end with those letters (e.g. cation is not ca- + -tion, gestion is not ges- + -tion), and they can be of either gender. (In this case, recognizing the suffix also tells you the pronunciation of the word: the suffix -tion is pronounced [sjɔ̃], but the letters “tion” are otherwise pronounced [tjɔ̃].)