First of all, you shouldn’t study the gender of a noun in the same way at all stages of our learning process. In the very beginning, you can go with the simple version: der Tisch, die Tür, das Bett. As long as you have an overseeable number of nouns to deal with, this works fine. The best way to do it is using images with the nouns and their articles. You can for example study flashcards with an image on one side and the noun and its article on the other side, or you can take photos of items, repeatedly go through them and try to recall their names and then check your answers with a list you made. It is also important to alternate the articles, since you need to get used to using all versions. The article ein might not be distinguishable between masculine and neuter but you still have to tie it to both types of nouns. What you study could look like this:
(image of a door) “Die Tür – Das ist eine Tür.”
(image of a table) “Der Tisch – Das ist ein Tisch.”
(image of a bed) ” Das Bett – Das ist ein Bett.” and so on.
It won’t be long until the number of nouns gets too high to keep studying like that though. At latest when you notice that you are starting to mix up the articles despite studying them regularly, start working with association. This means that you are not actually studying the article as a word but the gender of the noun. Assign a color to each gender, for example masculine – blue, feminine – red, neuter – yellow. Then connect the colors with the items. You can write down the nouns or put pictures of the items on sheets with the color of their gender. For example, take a red sheet and stick or draw pictures of a door, a lamp, a clock on it. Or write the nouns on a sheet and draw a red frame around it, or use a textmarker. You can also work with a memory palace here. Create three rooms in three different colors. Imagine how you are walking into the yellow room and you look at all the thing you put in there, a bed, a shelf, a glass, a book, all your neuter nouns. This works with tangible objects, actual things that you can visualize.
Make sure that the number of nouns you study at once is not too high. What you are able to memorize and automatize is an individual matter but if you go too fast, if you work with too many words all at once, your studying will be less efficient. Try maybe 8-20 nouns per week for intensive learning, that you repeat in the following weeks with longer pauses in between.
Later in your studies, there will be an increasing number of abstract words. Additionally, you will have to deal with cases, and that means that the numbers of articles you need to use increases as well. When you keep studying der, die, das, it won’t teach you using den (masculine accusative), dem (masculine dative), der (dative feminine) and so on without having to think about it. You have to include those other articles, as well as the possessive ones or the negative and demonstrative ones.
At this point, you need to study sentences, if you use clean cases. Clean cases are objects you use in a sentence that are directly tied to the verb (or in the genitive case to another object or subject). There are no prepositions here. Example: Wir haben einen Hund und ein Kaninchen. The dog (m.) and the rabbit (n.) are clean accusative cases. The idea is getting used to making sentences with the dog with as many articles as possible. A repetition chunk could look like this:
Das ist ein Hund. Wir haben einen Hund. Der Hund ist alt. Ich gebe meinem Hund einen Knochen.
Eventually, “eine Hund” or “einer Hund” will sound totally wrong to you. That is where you want to get.
Once you are familiar with fixed case prepositions (prepositions that always take the same case), you only need to study the prepositional phrases – that’s the preposition plus its object. This sentence element will never appear in any context in any other way. When combining mit + mein Hund, it will always be mit meinem Hund, no matter when, where and in which context. A repetition chunk could look like this:
mit meinem Hund, mit dem Hund, mit unserem Hund, mit einem Hund
You can also put different nouns in one repetition chunk with mit:
mit meinem Freund, mit meinem Fahrrad, mit dem Zug, mit einem Bus, mit meinen Kindern
When studying two-way (dual) prepositions, you need to use full sentences again, because the case of the object will depend on the verb you’re using, like the distinction of something taking place in one place (1) or movement to a place (2) or when you use verb-preposition combinations (3):
(1) Ich bin in der Stadt. Ich lebe in einer Stadt. In meiner Stadt gibt es ein Kino.
(2) Ich gehe in die Stadt. Wir fahren in eine Stadt. Kommen Sie in unsere Stadt!
(3) Sie wartet auf den Bus. Er wartet auf einen Bus. Wir warten auf unseren Bus.
This might seem like an awful lot of work, if you have collected many nouns over time that you need to study. Try to forget about the high number of nouns you need to study. Take out a few and concentrate on those. After repeating five sentences three times a day, a week later, you will have some of them down pat, maybe only one, and then you replace it with another one. Do that regularly and you will cover a lot of ground, and eventually use it correctly.
The alternative is to keep trying to remember the correct article pretty much every time you formulate a sentence for as long as you study German. Or you keep studying with der, die, das only and then regularly get the other articles wrong, often without even realizing it, because they don’t sound wrong to you. You need to get to the point where you can tell what sounds right or wrong, otherwise you cannot develop a natural relationship with the German language. It will always sound strange to you, and that will negatively impact your own production of the language, your writing and speaking.
With this method, you don’t just study the articles of course, you also get a lot of other material covered on the side, like which case to use with which preposition, a topic that many learners struggle with.
Keep in mind that studying the articles is always one of your main tasks when learning German, not just for beginners, but also for advanced students. It is not a complicated structure but it is very important for your language development.