Dans la salade, j’ajoute des radis et une vinaigrette au citron.

Dans la salade means in the salad or into the salad.

French often uses dans to show where something is being put:

• mettre quelque chose dans... = to put something in...
• ajouter quelque chose dans... = to add something into...

Here, Dans la salade sets the scene first: as for the salad / in the salad, I add...

It is very natural, especially in recipes or cooking instructions.

Because je becomes j’ before a vowel sound.

Since ajoute starts with a, French uses elision:

• je ajoute → j’ajoute

This is the same pattern as:

• j’aime
• j’habite
• j’écoute

Because des radis and une vinaigrette au citron are the direct objects of ajoute.

You are adding what?

• des radis
• une vinaigrette au citron

So no preposition is needed before those nouns.

French can also use ajouter quelque chose à quelque chose:

• J’ajoute du sucre au café.
  = I add sugar to the coffee.

In your sentence, the destination is expressed separately with Dans la salade, so the structure is perfectly natural.

Des is the plural indefinite article, meaning some.

So:

• un radis = a radish
• des radis = some radishes

It is used because we are talking about radishes in a general, non-specific way.

Compare:

• les radis = the radishes (specific radishes already known)
• des radis = some radishes

Here it is plural because of des: des radis.

The word radis is one of those French nouns whose singular and plural are spelled the same:

• un radis
• des radis

In pronunciation, they are usually the same too:

• radis → roughly ra-dee

So the article tells you whether it is singular or plural.

Both can be possible in French, but they do not feel exactly the same.

• une vinaigrette suggests a vinaigrette / one dressing / one kind of dressing
• de la vinaigrette suggests some vinaigrette as an uncountable substance

In a sentence like this, une vinaigrette au citron sounds like:

• a lemon vinaigrette
• a lemon dressing

So French is treating it as a kind or type of dressing, which is very natural.

Here au citron means with lemon or lemon-flavored.

In food French, à / au / aux is very often used to describe an ingredient or flavor:

• gâteau au chocolat = chocolate cake
• yaourt à la vanille = vanilla yogurt
• vinaigrette au citron = lemon vinaigrette

So this does not mean to the lemon. It is just the normal French way to describe flavor or main ingredient in many food expressions.

Because au is the contraction of à + le:

• à + le = au

The noun citron is masculine:

• le citron

So:

• à + le citron → au citron

Compare:

• à la vanille (because vanille is feminine)
• aux herbes (because herbes is plural)

Putting Dans la salade first gives a slightly more natural recipe-style or instructional feel.

It highlights where the ingredients are being added before saying what is added.

A more neutral order could be:

• J’ajoute des radis et une vinaigrette au citron dans la salade.

That is understandable, but beginning with Dans la salade sounds smoother here and helps frame the action right away.

The comma separates the introductory phrase Dans la salade from the main clause.

So the structure is:

• Dans la salade, = introductory location phrase
• j’ajoute des radis et une vinaigrette au citron. = main statement

This comma is common when a short phrase is moved to the front for clarity or emphasis. In informal writing, some people might omit it, but using it here is perfectly normal.