When is "to" a preposition and when the infinitive marker?

• I want to see you.
• I look forward to seeing you.

How can one say "to" in the first sentence is an infinitive marker and in the second sentence a preposition when we are given just the following two sentences and are asked to fill in the blanks?

• I want to ____(see/seeing) you.
• I look forward to __(see/seeing) you.

Having written this, I've just noticed Barrie's answer. By far the easiest thing to do is to learn the constructions, but they can be analysed (as Bill Franke asked in a comment). Whether it's actually worth the effort may be a moot point.

Let's deal with the second sentence first, because that's easier.

The second sentence uses the phrasal verb look forward. While this idiomatic verb means anticipate, it behaves grammatically and requires a preposition to indicate the indirect object — what you are looking at, or in this case, looking forward to (it's "to" because it's concerned with time).

Thus look forward requires to as a preposition and a noun or noun phrase. See is a verb and therefore not right; seeing is a gerund behaving as a noun and is therefore the right form to use.

I look forward to seeing you.

The first sentence has a wrinkle or two. Want is not a simple verb!

Where a verb is followed by a second verb, that second verb is always in an infinitive form. Because want is not a modal verb (such as do or can) that infinitive form uses to.

I can have it [can is never followed by a to infinitive]
I want to have it [want is followed by a to infinitive]

Want can also be followed by a noun, or noun phrase, or a gerund which acts as a noun; that is, it can be an ordinary transitive verb.

I want an apple
That last cake wants eating

In this case, seeing you is not a noun phrase or gerund, it's a present participle and thus ungrammatical. Therefore the next word must be an infinitive form of the verb (see) and because of that it needs to.

I want to see you.

The wrinkle is knowing that seeing presented as a choice here is a present participle and not a gerund like the "look forward" sentence. The clue is that it has its own object, you, which conflicts with the use of want. Want fundamentally indicates a need, a lack, which must be satisfied. As such, it can only have a single object, the one thing which satisfies that need, so you can't use seeing you. Thus you must use see and that must be a to infinitive.

Want is one of a group of verbs that commonly occur with a to-clause rather than a that-clause. English doesn’t allow a sentence like ‘I want that I see you.’ It has to be ‘I want to see you.’

Look forward to is what the ‘Longman Student Grammar of Spoken and Written English’ calls a phrasal-prepositional verb. That is, it consists of a verb followed by an adverbial particle, followed by a preposition. It can be followed by a noun phrase (‘I’m looking forward to the match’) or by the -ing form of a verb (‘I’m looking forward to seeing you’), but not by to + infinitive.

The simplest way of knowing the difference is to learn the constructions which each verb allows.

I know that giving rather strange rules which demand quite different analyses of similar-looking constructions can seem worrying / bewildering / infuriating. Perhaps if we look at near-paraphrases it will help a little (perhaps not):

2. I look forward to seeing you.

The string look forward is rarely used without the to (it would then be a less opaque idiomatic usage - don't look at what has happened in the past; look forward/s - and then ahead would probably be preferred anyway). (Google searches for "look forward to" and "look forward" -"look forward to" lend reasonable support to this claim.)

Look forward to has the fairly opaque (not too guessable from its component words) idiomatic meaning, eagerly anticipate. I'd say it has a unitary meaning (although in this case, I can only think of a two-word 'synonym', not a single word one - and perhaps 'anticipate quite eagerly' is closer in sense). Some would class the three-word string as a transitive multi-word verb (and possibly reclassify the to as a particle if pressed to parse individual words).

Notice that a noun as well as an -ing group could occupy the object space:

I look forward to seeing you.

I look forward to playing.

I look forward to the concert.

1. I want to see you.

Here, although there are again arguments for considering want to as a unit (He helped wash up / he helped to wash up; I want to go / je désire aller; But I want to!) there are considered to be more persuasive reasons for us to consider the to as more tightly bound to the base form of the following verb (to make a to-infinitive rather than the bare infinitive):

To see you tomorrow is impossible.

What do I want most? To see John.

I intend to see him tomorrow.

?/* Sorry, what did you say you intend?

Sorry, what did you say you intend to do?

*Sorry, who did you say you intend to?

Sorry, who did you say you intend to see?

*I intend to the concert.

The second one is a "tri-part phrasal verb" and always takes a noun phrase after it. I look forward to + seeing you/the movie/seeing the movie with you. Does that make sense?

Want will often take an infinitive after it. I want to see the movie.