kyou ha tamago no tokubai desita ga, watasi ga itta toki ni ha mou urikire desita.

は marks 今日 as the topic of the sentence.

So 今日は means something like:

• As for today, ...
• more naturally in English, just Today, ...

It sets the scene for what follows. In this sentence, the speaker is talking about what the situation was today.

卵の特売 means a sale on eggs or eggs being on special.

Here, の links two nouns:

• 卵 = eggs
• 特売 = special sale, bargain sale

So 卵の特売 is literally something like egg sale, meaning a special sale involving eggs.

This use of の is very common in Japanese for connecting nouns.

Yes, 特売 is a noun. In Japanese, nouns can be used as predicates with です / でした.

So:

• 特売です = it is a special sale
• 特売でした = it was a special sale

In context, 今日は卵の特売でした means:

• Today, eggs were on sale
• or There was a special sale on eggs today

This is very natural Japanese.

Here, が means but.

So:

• 今日は卵の特売でしたが、... = Today there was a sale on eggs, but...

This が connects two clauses and shows contrast.

It can sound a little softer or more formal than just using でも at the start of the next sentence.

In 私が行ったとき, the clause 私が行った modifies とき.

Inside this kind of embedded clause, が is often used to mark the subject:

• 私が行ったとき = when I went

Using は here is not impossible in every context, but が is the normal choice when you are simply identifying who did the action inside the clause.

So this is not saying as for me, I went with strong topic marking. It is simply marking I as the subject of went.

This is a very common question.

• 行くとき = when I go / when I’m about to go
• 行ったとき = when I went / when I had gone

In this sentence, the speaker is referring to the time they actually arrived or went to the store and found the eggs sold out. So 行ったとき is the natural choice.

A rough nuance here is:

• 私が行くときには = when I was going / when I was about to go
• 私が行ったときには = by the time I went / when I got there

とき means time or when.

So:

• 行ったとき = when I went
• 行ったときに = at the time when I went / when I went

The に marks a point in time. In many sentences with とき, this に is optional.

So these are both possible:

• 行ったとき、もう売り切れでした
• 行ったときに、もう売り切れでした

The version with に can sound a little more explicit, but the meaning is basically the same here.

には is に + は.

• に marks the time point
• は adds topic or contrast

So 行ったときには has a slight contrastive feeling, something like:

• when I went, though...
• by the time I went...
• as for the time when I went...

In this sentence, that contrast fits well: there was a sale, but by the time the speaker went, the eggs were already sold out.

Here, もう means already.

So:

• もう売り切れでした = it was already sold out

This is different from the common negative pattern:

• もうない = there isn’t any more
• もう行かない = I won’t go anymore

With a positive statement like this one, もう usually means already.

Both are related, but they are slightly different in feel.

• 売り切れる is a verb meaning to sell out
• 売り切れ can also refer to the sold-out state

So:

• 売り切れました = it sold out
• 売り切れでした = it was sold out

In this sentence, the speaker is describing the condition at the time they went to the store: the eggs were already sold out. That is why 売り切れでした works very naturally.

Not directly, but it is understood from context.

The first half mentions 卵の特売. So in the second half, もう売り切れでした naturally means that the eggs on sale were sold out.

Japanese often leaves out things that are already clear from context. In English, we might repeat the eggs, but in Japanese that repetition is often unnecessary.

It breaks down like this:

• 今日は = as for today
• 卵の特売でしたが、 = there was a sale on eggs, but
• 私が行ったときには = when I went / by the time I went
• もう売り切れでした。 = they were already sold out

So the whole sentence is built as:

• topic/background
• contrast with が
• time clause
• result/state

That is a very common Japanese sentence pattern.