Hoy quiero ir a la heladería del paseo y pedir un helado de vainilla.

Hoy means today. It sets the time frame right away.

You do not always need it, because Spanish can often leave out obvious time words if the context is clear. But here it helps make the sentence more natural and specific: Today I want to go...

Spanish very often puts time expressions like hoy, mañana, or esta tarde near the beginning of the sentence.

Spanish often leaves out subject pronouns because the verb ending already shows who the subject is.

• quiero = I want
• quieres = you want
• quiere = he/she/it wants

So Hoy quiero ir... already clearly means Today I want to go...

You could say Hoy yo quiero ir..., but that usually adds emphasis, contrast, or emotion, such as I want to go, not someone else.

Quiero is the 1st person singular present indicative of querer.

So it means:

• I want
• sometimes I would like, depending on context

Querer is a stem-changing verb:

• yo quiero
• tú quieres
• él/ella quiere
• nosotros queremos
• vosotros queréis
• ellos quieren

The e → ie change happens in most forms, but not in nosotros and vosotros.

After querer, Spanish normally uses an infinitive when the subject of both verbs is the same.

So:

• Quiero ir = I want to go
• Quiero pedir = I want to order

This is the same basic idea as English want to + verb.

If the subject changes, Spanish often uses que + a conjugated verb:

• Quiero ir = I want to go
• Quiero que vayas = I want you to go

The verb ir normally uses a before a destination:

• ir a casa
• ir al supermercado
• ir a la playa
• ir a la heladería

So ir a la heladería means to go to the ice cream shop.

This a is required with destinations. It is not optional here.

In Spanish, articles are often used more regularly than in English.

Heladería is a feminine noun, so it takes la:

• la heladería = the ice cream shop

In this sentence, la suggests a specific shop, not just any ice cream shop. The phrase del paseo narrows it down even more: it is the one associated with the promenade/walk.

They are related, but they are not the same word:

• heladería = ice cream shop / ice cream parlour
• helado = ice cream

A useful pattern here is:

• -ería often refers to a shop or place associated with something

For example:

• pan → panadería = bakery
• zapato → zapatería = shoe shop
• helado → heladería = ice cream shop

So in the sentence:

• ir a la heladería = go to the ice cream shop
• pedir un helado = order an ice cream

Because de + el contracts to del in Spanish.

So:

• de el paseo → del paseo

This contraction is mandatory.

Spanish has two common contractions:

• a + el = al
• de + el = del

But this only happens with el, not with la, los, or las:

• de la plaza
• de los niños
• de las tiendas

Paseo can mean several related things depending on context, such as:

• a walk
• a stroll
• a promenade
• a boulevard or pleasant walking area

In la heladería del paseo, it most naturally refers to the ice cream shop on/by the promenade or the one associated with the paseo.

Spanish often uses de in place names or location phrases where English might prefer on, by, or at.

The basic meaning of pedir is to ask for. In contexts like food, drinks, or items in a shop, it naturally becomes to order.

So:

• pedir un café = order a coffee
• pedir la cuenta = ask for the bill
• pedir ayuda = ask for help

In this sentence, pedir un helado means to order an ice cream.

Helado is a masculine singular noun, so the indefinite article is un:

• un helado = an ice cream

If it were plural, it would be:

• unos helados = some ice creams

If you were talking about ice cream in a more general or mass-noun way, Spanish might use different structures depending on the meaning, but here un helado clearly means one ice cream / an ice cream.

Spanish often describes flavours with de + noun:

• helado de vainilla = vanilla ice cream
• helado de chocolate = chocolate ice cream
• zumo de naranja = orange juice

So de vainilla literally means of vanilla, but in natural English we say vanilla.

This structure is extremely common in Spanish for flavours, materials, and contents.

Yes, in context it means something like:

• I want to go to the ice cream shop and order a vanilla ice cream

The y simply links the two actions:

1. ir a la heladería
2. pedir un helado de vainilla

Spanish often uses this straightforward verb + y + infinitive structure when one person wants to do two related actions.

You could also say para pedir if you want to make the purpose more explicit:

• Hoy quiero ir a la heladería del paseo para pedir un helado de vainilla.

That would mean Today I want to go to the ice cream shop on the promenade to order a vanilla ice cream.

A few useful pronunciation points:

• h is silent in Spanish, so heladería starts like el...
• The stress in heladería falls on rí: he-la-de-RÍ-a
• In much of Spain, ll is pronounced similarly to the English y sound, so helado and heladería usually sound with a y-like sound if relevant
• paseo is pronounced roughly pa-SE-o, with the vowels clearly separated

A simple learner-friendly pronunciation of the whole sentence would be:

oy KYE-ro eer a la e-la-de-RI-a del pa-SE-o ee pe-DEER oon e-LA-do de bai-NI-ya

Exact regional pronunciation varies, but that version will be understood.

Yes, it is natural and correct.

A speaker in Spain might also say slightly different versions depending on style or situation, for example:

• Hoy quiero ir a la heladería del paseo y pedir un helado de vainilla.
• Hoy me apetece ir a la heladería del paseo y pedir un helado de vainilla.
  = Today I feel like going...
• Hoy quiero pasar por la heladería del paseo y pedir un helado de vainilla.
  = Today I want to stop by the ice cream shop...

But your original sentence is perfectly good, clear Spanish.