The Spanish verb for both meeting someone for the first time and knowing someone is conocer. This causes problems and creates confusion if the two get mixed up. Take this phrase as an example:

I want to meet her.
Quiero conocerla.
kee-ehr-oh koh-noh-sehr-lah.

But notice how the following phrase has the same Spanish translation even though the meaning in English is different:

I want to know her.
Quiero conocerla.
kee-ehr-oh koh-noh-sehr-lah.

Since conocer is also used for both meeting or knowing someone the way to clarify that is using conocer with llegar (to arrive):

I want to (get to) know her.
Quiero (llegar a) conocerla.
kee-ehr-oh (yeh-gahr ah) koh-noh-sehr-lah.

Another way that changes the context is using mejor (“better”). This will make it clear you are talking about wanting to “know you” rather than just “meet you.” Like if you’ve had contact by phone or on-line but haven’t met in person yet:

I want to know you better.
Quiero conocerte mejor.
kee-ehr-oh koh-noh-sehr-teh meh-hohr.

When talking about the past the actual meaning of conocer changes depending how you conjugate conocer. (Whether you’re using the preterite or imperfect past tense):

I met her three years ago.
La conocí hace tres años. (preterite form)
lah koh-noh-sEE ah-seh trehs ahn-yohs.

I knew her for three years.
La conocía por tres años. (imperfect form)
lah koh-noh-sEE-ah pohr trehs ahn-yohs.

The above phrase could be used in examples where someone moved away and you lost contact. That conjugation of conocer is also handy for phrases like this:

There were a lot of people at the party but I didn’t know them.
Había mucha gente en la fiesta pero no los conocía.
ah-bEE-ah moo-chah hehn-teh ehn lah fee-ehs-tah peh-roh noh lohs koh-noh-sEE-ah.

If you’re talking about friends or someone you still have contact with you can use this:

I’ve known her for three years.
La conozco desde hace tres años.
lah koh-nohs-koh dehs-deh ah-seh trehs ahn-yohs.

or:

We’ve known each other for three years.
Nos conocemos desde hace tres años.
nohs koh-noh-seh-mohs dehs-deh ah-seh trehs ahn-yohs.

So conocer is used for meeting someone for the first time. What about “meeting someone” you already know at a specific place or time? In that case you don’t use conocer, you can use a different verb like encontrarse instead:

Let’s meet at the park.
Nos encontramos en el parque.
nohs ehn-kahn-trah-mohs ehn ehl pahr-keh.

Since encontrarse is an ar verb when you use it in the first person plural form (we, us) it conjugates the same for the present or the preterite:

We met at the park.
Nos encontramos en el parque.
nohs ehn-kahn-trah-mohs ehn ehl pahr-keh.

Notice how the Spanish translation is the same for both the above phrases? For context you can just add something to the phrase:

We met at the park last week.
Nos encontramos en el parque la semana pasada.
nohs ehn-kahn-trah-mohs ehn ehl pahr-keh lah seh-mah-nah pah-sah-dah.

In the above examples the context is this is a person you already know. If this was the first time meeting this person you would say:

We met (for the first time) at the park.
Nos conocimos en el parque.
nohs koh-noh-see-nohs ehn ehl pahr-keh.

Lastly, we’ll combine a couple things we’ve discussed above:

Let’s meet at the cafe and get to know each other better.
Nos encontramos en el café y llegar a conocernos mejor.
nohs ehn-kohn-trah-mohs ehn ehl kah-fEH y yeh-gahr ah koh-noh-sehr-nohs meh-hohr.

In my last post I talked about the difference between parecer and parecerse and used some examples of how paracer means “to seem” (ex: you seem angry) or “to look” (ex: you look jealous). If your not familiar with parecer read my previous post.

For parecerse (the reflexive version of parecer) you want to use it when comparing someone to another specific person. So instead of “to seem” it means “to resemble,” “to be similar” or “to be alike.” It’s commonly used for comparing peoples appearance. So if you are talking to someone and they are with a friend you could say:

You look like your friend.
Te pareces a tu amigo/a.
teh pah-reh-sehs ah too ah-mee-goh/ah.

Or you can flip it around:

Your friend looks like you.
Tu amigo/a se parece a ti.
too ah-mee-goh/ah seh pah-reh-seh ah tee.

You could respond with:

I don’t look like [him/her].
No me parezco a [él/ella].
noh me pah-rehs-koh ah [EHl/eh-yah].

A different example:

Last night I saw someone that looks like you.
Anoche vi a alguien que se parece a ti.
ah-noh-cheh vee ah ahl-gee-ehn keh seh pah-reh-seh ah tee.

Notice the a in the sentence after te pareces and se parece and me parezco. You use the a to connect the two people that are being compared to each other. You always have to include that when using parecerse if you are comparing a specific person in the beginning of the phrase to another specific person at the end of the phrase. 

Here’s another way to use parecerse:

You two look alike.
Ustedes se parecen.
oo-steh-dehs seh pah-reh-sehn.

You two don’t look at all alike.
Ustedes no se parecen en nada.
oo-steh-dehs noh seh pah-reh-sehn ehn nah-dah.

No a required here because you’re not saying “You look like him” or “You look like her” – you aren’t comparing a person in the beginning with a person at the end.

You can even use parecerse to ask what someone looks like:

What does [he/she] look like?
¿A qué se parece? (literally: What does he/she resemble?)
¿ah kEH seh pah-reh-seh?

So what about a phrase like “You look Latino”? Since you’re not comparing them to any specific Latino you would use parecer:

You look Latino. (or seem Latino)
Paraces latino.
pah-reh-sehs lah-tee-noh.

But if you point out a specific person, then use parecerse:

You look like Shakira.
Te pareces a Shakira.

Parecerse can also be used for comparing things besides people:

Spanish and Italian are a lot alike.
El español y el italiano se parecen bastante.
ehl ehs-pahn-yohl ee ehl ee-tah-lee-ahn-oh seh pah-reh-sehn bahs-tahn-teh.

When it comes down to talking about people use parecer for general descriptions (ex: “you look young” or “you seem drunk”) but use parecerse when talking about the similarity between two specific people (ex: “you look like María”).