I'd like to say “Tomorrow is Monday”. Is it correct for me to say 「あしただげつようび」? Or is there simply no particle at all?
No, you can't use だ that way.
Here's what you're trying to do:
Unfortunately, that doesn't work. Why not?
So what can you do?
Feel free to stop reading here. Go to a store and buy a textbook, or sign up for a class! You'll learn a lot more that way. But because I feel like writing, and because it's educational for me to articulate my thoughts, I'll do my best to answer your question anyway.
A comparison between English and Japanese
To understand what's different between English and Japanese, we first have to understand what's going on in English. Let's take a look at your sentence:
The verb "is" is called a "copular verb". The "copula" part comes from Latin, and it literally means that it joins two things together. When you say "A is B", you're joining A with B somehow. And of course, the copula has a lot of uses in English. Here are a couple important ones:
What about Japanese? Does it have something similar? Well, だ is often described as the copula! And in fact, it does something pretty similar, joining two things together. But there are two big differences:
So you can't just stick だ where you'd stick is, even though it's pretty similar.
In Japanese, we usually put predicators at the end of a sentence. But wait, what's a predicator? Well, in English, we really only have one type of word that can be a predicator, and that's a verb! But Japanese has three types:
The key here is that the predicator comes at the end, no matter which type of word it is. Of course, there's a lot more to say about these examples, and of course I want to focus on the noun + copula combination. But first, we'll have to take a look at some of the other words in these sentences.
You'll notice something about the words ストア, これ, and そら. All three of these are marked with a suffix that tells you what role it plays in the sentence. In example 1, for instance, we've got the suffix に ("to") attached to the noun ストア ("store"):
These suffixes are usually called particles. And when you add one of these suffixes, it makes a new "phonological word". In less technical terms, that means you should pronounce the -ga in sora-ga as though it's part of the same word! Let me repeat this, because it's really important:
When you pronounce sora-ga, do not pause after sora!
And だ is a special kind of suffix, too. When we add だ to リンゴ ("apple"), we get the predicator リンゴだ ("is an apple"). And again, you can't pause between リンゴ and だ. Phonologically speaking, the combination is a single word! And like all predicators, リンゴだ has to come at the end of the sentence. We can't stick it in the middle.
What about your sentence?
Well, there are more things we need to learn before we can fix it, but I'm sure you can see one problem with it now. When you add だ to あした ("tomorrow"), you get a predicator あしただ ("is tomorrow"). And that has to come at the end of the sentence! So by the time you start saying げつようび, your sentence is already over. This is no good.
Instead, we probably want to attach だ to the second word and form the predicator げつようびだ ("is Monday"). So if we do that, your sentence looks something like this:
Well, that's still not perfect, but it's an improvement. You could get away with saying this, but it's not quite complete. I put in a ∅ symbol to show where something has been left out. But before I talk about what to add to make it complete, I want to talk about English again.
Subjects and predicates
The terms subject and predicate come from western grammar. The idea is that the predicate says something about the subject. For example, it can say something that the subject is doing (like "goes to the store"), or it can tell us about a trait (like "is green"). Let's look at your sentence:
The subject is "tomorrow". The predicate is "is Monday". That tells us something about the subject, right? Well, that's what predicates do. (Remember, our English predicator is the verb "is". The whole predicate is "is Monday".)
In English, we know that "tomorrow" is the subject because it's a noun and because it's at the beginning of the sentence. We're pretty good at spotting subjects, even though we don't mark them with a suffix in English. So it's easy for us to see what part of the sentence the predicate is acting on.
And in Japanese, we have predicates too. And a predicate contains a predicator, just like in English. The difference is what a predicate acts on. In Japanese, you mark the thing a predicate acts on using a particle. And usually, it's one of these two:
In English, both the subject "the sky" and the topic "this" would be expressed grammatically as a subject. So here again, you can see a difference between English and Japanese grammar.
Completing the sentence
Let's go back to your sentence. We saw earlier that あした was missing something:
How do we tell whether we should add は or が? Well, unfortunately the difference is too complicated to explain here. And it's notoriously difficult to explain, and controversial to boot, so I'd probably end up explaining it wrong. (Entire books have been written on the subject!) But since you're just starting out, you don't need to worry about that yet. You need to learn some sentence patterns and grammar before you delve too deep into the mystery of は versus が.
So for now, let's just say that we want to add the topic particle は! Let's add that in:
And now we've got a complete sentence! Woo hoo! Our predicator げつようびだ ("is Monday") tells us something about the topic あした. We can say that the right half of the sentence is "predicating on" the left half. (And remember, pronounce ashita-wa as one word, and the same goes for getsuyōbi-da! Don't pause!)
So this sentence is done. But remember: textbook, class, or website ;-)
In this answer, * means that the sentence is not grammatical Japanese.