The Spanish /r/ sound is written with the letter 'r'—but don't let that fool you. The Spanish /r/ has nothing to do with the English /r/. Using your English /r/ in Spanish produces an incomprehensible accent. Fortunately, you already know how to make the Spanish /r/.
1. How to make it
Say the words buddy, petty, hotter rapidly, without overly precise articulation of the d's and t's. Can you feel what your tongue does in the middle of each word? It taps the roof of your mouth. (If you're not sure, freeze right in the middle of buddy.) That tap is the Spanish /r/.
Start with the word Beri (a Spanish name). It's pronounced almost exactly like the English name Betty.
Now try "para", which is pronounced very much like "spot a hawk", if you omit the 's' and the 'hawk'.
So you see that you already know how to make Spanish /r/ and it has nothing to do with English /r/. The main challenge is that in English, this tap occurs only in the middle of words, but in Spanish it occurs in many contexts. Try these:
If you're having trouble making the tap right next to a consonant (eg., gracias), try adding a little space before the tap: guh-racias and then gradually eliminate it: g...racias, g..racias, g.racias, gracias.
2. When to make tap /r/
Although tap /r/ is always written with the letter 'r', 'r' sometimes implies a trilled /r/. How do you know when to tap and when to trill? The rules are pretty simple:
A. The tap is obligatory in-between vowels within a word (eg., caro, pero), because that is where single 'r' contrasts with the double 'rr' trill (eg., carro, perro).
B. The tap is obligatory following a consonant (eg., abre, crema).
C. The tap is optional before a consonant (eg., puerta, mercado) or at the end of a word (eg., mar); trill may also be used in those places, especially for emphasis.
D. The tap is never used at the beginning of words. Initial 'r' (eg., rojo, ridículo) always implies a trill.
The other 23 sounds of Spanish ...
This lesson on the Spanish tap R is included in the SuperCoco app, which also covers the other twenty-three sounds of Spanish—nineteen of which are different from English. The pronunciation course is part of SuperCoco's overall approach teaching Spanish through conversations
—with training wheels
on. Read more about it here...