De boormachine ligt onder de gordijnrail.

Dutch often uses a position verb where English would simply say is.

• liggen = to lie, to be lying
• staan = to stand, to be standing
• zitten = to sit, to be located/fitted
• zijn = to be

In De boormachine ligt onder de gordijnrail, ligt suggests the drill is in a lying position somewhere under the curtain rail.

So Dutch prefers:

• De boormachine ligt daar. = The drill is there / is lying there.

Using is would usually sound less natural here unless you are talking more abstractly about existence or identity, not physical position.

Ligt is the third person singular present tense of liggen.

The subject is de boormachine, which is singular, so you use:

• ik lig
• jij ligt
• hij/zij/het ligt
• de boormachine ligt

So the verb agrees with the singular noun.

In Dutch, every noun has grammatical gender, and this determines whether it takes de or het in the singular.

Boormachine is a de-word, so:

• de boormachine

Unfortunately, for many nouns you simply have to learn whether they are de or het.

A useful pattern here is that many nouns ending in -machine are de-words:

• de machine
• de wasmachine
• de boormachine

In the plural, all nouns take de anyway:

• de boormachines

Boormachine is a compound noun:

• boor = drill
• machine = machine

So literally it means something like drilling machine, but in normal English the natural translation is simply drill.

Dutch uses compound nouns very often, much more openly than English learners may expect.

Gordijnrail is also a compound noun:

• gordijn = curtain
• rail = rail / track

Together:

• gordijnrail = curtain rail / curtain track

In Dutch, compound nouns are usually written as one word, whereas English often writes them as two words or with variation.

So:

• gordijn + rail = gordijnrail

This is completely normal in Dutch spelling.

Gordijnrail is also a de-word, so the sentence uses:

• de gordijnrail

With Dutch compound nouns, the last part usually determines the grammatical gender and plural behavior.

Since rail is a de-word:

• de rail
• therefore de gordijnrail

This is a very useful rule for compounds.

Onder means under.

In this sentence it introduces a prepositional phrase:

• onder de gordijnrail = under the curtain rail

It does not force special word order here. The basic structure is:

• De boormachine = subject
• ligt = verb
• onder de gordijnrail = location

So the sentence follows a very normal Dutch main-clause pattern: subject + verb + rest

In a normal main clause, Dutch puts the finite verb in the second position.

So:

• De boormachine = first element
• ligt = second element

That gives:

• De boormachine ligt onder de gordijnrail.

The version De boormachine onder de gordijnrail ligt is not normal as a standalone main clause.

However, in a subordinate clause, the verb often moves to the end:

• Ik zie dat de boormachine onder de gordijnrail ligt.
• I see that the drill is under the curtain rail.

In this sentence, it clearly means location, not movement, because of ligt.

• ligt onder de gordijnrail = is lying under the curtain rail

If you wanted to express movement to that place, Dutch would normally use a movement verb, for example:

• De boormachine valt onder de gordijnrail. = The drill falls under the curtain rail.
• Hij schuift de boormachine onder de gordijnrail. = He slides the drill under the curtain rail.

So onder itself can appear in both kinds of situations, but the verb tells you whether the meaning is static or dynamic.

Usually yes, if the drill is resting horizontally or just thought of as lying somewhere.

Dutch chooses among position verbs based on how something is positioned:

• liggen for things lying flat or conceived as lying
• staan for things standing upright
• zitten for things attached, contained, stuck, or fitted somewhere

So depending on the situation, you could also hear:

• De boormachine staat in de kast. = The drill is in the cupboard.
  (perhaps upright)
• De boormachine ligt in de kast. = The drill is in the cupboard.
  (perhaps lying on a shelf)

English often uses is in both cases, but Dutch usually makes a more specific choice.

A rough pronunciation guide is:

• De ≈ duh
• boormachine ≈ BOR-ma-shee-nuh
• ligt ≈ likht
• onder ≈ ON-der
• de ≈ duh
• gordijnrail ≈ gor-DINE-rail

A few notes:

• oo in boor is a long o sound.
• g in standard Dutch is a throaty sound, harder than English g.
• ij in gordijn sounds somewhat like the vowel in line for many learners, though not exactly.
• Final -e in words like machine is usually a weak uh sound.

Yes. That would mean:

• There is a drill under the curtain rail.

The difference is mainly in focus:

• De boormachine ligt onder de gordijnrail.
  You are talking about the drill specifically.
• Er ligt een boormachine onder de gordijnrail.
  You are introducing the existence/presence of a drill there.

Both are natural, but they serve slightly different purposes in conversation.