One of the best ways to learn introductory French vocabulary is to learn set phrases that are commonly used. For instance: "Qu'est-ce que c'est ?" means "What is this?" There is also the related question-asking phrase "est-ce que?", as in: "Est-ce qu'on viendra ce soir?" ("Are they coming this evening?")
Learn other common phrases, like "je m'appelle" ("my name is") and "Comment vous appelez-vous?" ("what is your name?"), "j'ai __ ans" ("I am __ years old." This can help you learn your first number; for instance, eighteen---dix-huit) and "je suis américain/e" ("I'm an American;" masculine/feminine).
Learning whole phrases helps you speak in French more quickly, while also passively teaching you sentence structure and verb conjugations. For more French phrases, see Resources below.
Divide up your learning of French vocabulary by theme or topic. This gives you a limited number of words to work on at one time, and you can use them together logically. For instance, focus on garden vocabulary, learning words like le jardin (garden), l'herbe (grass), la fleur (flower), le sol (soil), les insectes (insects), les légumes (vegetables), les fruits (fruits), la brouette (wheelbarrow), la truelle (trowel), la pelle (shovel), les gants (gloves), le soleil (sun), l'eau (water) and l'arrosoir (watering can). When learning concrete vocabulary---words for things you can touch---you can label them so you frequently see their French equivalents.
From this, you can see that you should learn French nouns along with their definite article so you can always remember their gender. This is important, as gender is less intuitive than in languages like Spanish and Italian.
You can also incorporate verbs and other appropriate parts of speech into thematic vocabulary. For instance, "Je travaille dans le jardin" ("I am working in the garden"). For some French vocabulary lists, see Resources below.
For people who like highly organized learning, you may want to separate your study into parts of speech. This works best for parts of speech that have multiple components, such as nouns and adjectives in gender and number, conjugated verbs in their tenses and irregular verbs, along with parts of speech that have limited numbers of words, like prepositions and pronouns.
For instance, when studying verbs, study only one tense in its full conjugation at one time. If you're studying the simple past, select a regular verb and learn its full simple past conjugation. Let's use aimer (to like or love): j'aimai, tu aimas, il aima, nous aimâmes, vous aimâtes, ils aimèrent. This teaches you the simple past endings for -er verbs, and, at the same time, supports your knowledge of pronouns.
Use audio resources to get the most out of your French vocabulary learning. By using audio resources, you improve your own pronunciation as well as your listening comprehension. To hear any word in the French language pronounced, you can use Promt Online Translation's text-to-speech service (see Resources below); simply type in your word and click the megaphone icon.
No matter what learning resources you're using, keep a detailed and organized notebook of vocabulary you learn. Writing words down helps you remember them, and organizing them will help you review them more easily later.