Before we can really get started, we need to understand an important fact about Latin: it's what's known as an inflected language. This essentially means that a word's function in a sentence is based on the way that word ends. Nouns and verbs are categorised according to these endings, and for each category there are specific patterns for modifying the word to fit the sentence. Since we only have one verb in the phrase we want to translate, let's focus instead on the nouns.
A noun in Latin has three essential attributes: case, number, and gender. The case tells us the noun's use in the sentence, and there are six – nominative, genitive, dative, accusative, ablative, and vocative. Each case is appropriate to different circumstances, but here we'll only need the nominative case. Number is straightforward: do we have one of the noun (singular) or more than one (plural)? Mercifully, we're only dealing with singular nouns here. Gender is a little more complicated: in Latin, a noun is either masculine, feminine, or neuter. Now, in some cases, the grammatical gender of a Latin word corresponds to the gender of its meaning: puer (boy) is masculine in both, while puella (girl) is feminine in both. In other cases, the grammatical gender actually conflicts with the gender of the meaning, but most of the time (at least to anglophone eyes), the assignment of gender seems fairly arbitrary – digitus (finger) is masculine, fenestra (window) is female, and caelum (sky) is neuter. Really, we just need to remember that Latin words have this characteristic, and that it's important. By knowing these attributes, we can determine the category (the declension) to which the noun belongs, and so determine how to properly modify the word's ending to fit a sentence.
With this in mind, we're ready to translate, so let's divide the sentence into its two clauses, and take them each one word at a time:
My (pronoun) • Little (adjective) • Pony (noun)
Friendship (Noun) • is (verb) • Magic (noun)
Rather than go in word order, let's start with pony, since it's the subject of the first clause. In pieces of fandom artwork that call for a fancy-looking Latin motto, I've often seen equus used. This is the Latin word for horse (hence Equestria), but to me, horse doesn't convey quite the right meaning. Obviously we're dealing with a specific kind of horse: a pony, the proper word for which in Latin is mannus. Admittedly, mannus is used far less frequently in Latin literature than equus (though it does make a memorable appearance in one of Pliny the Younger's letters), but it's far more accurate for our purposes.
We can take this word a step further by using its diminutive form, which not only further indicates smallness (we are dealing with little ponies, after all), but also a sense of affection. As an example: the name by which the emperor Caligula is commonly known is the diminutive form of the word caliga. He gained this nickname (or cognomen) as a boy; it's said that while out on military campaigns with his father Germanicus, he so delighted in warfare that a miniature uniform was made especially for him. Thus he became known fondly by the troops as caligula, or little boot. In the case of mannus, we get mannulus, which is nominative, singular, and masculine.
By using the diminutive form of mannus, we've already helped establish the "little" aspect of our phrase. Still, we'd do well to further enforce it by using the Latin adjective for little, parvus, which matches the noun it modifies in case, number, and gender (note the -us ending shared by the two words). We could even use its diminutive form parvulus if we liked, though that would likely only be appropriate for the Cutie Mark Crusaders, or perhaps Applejack after exposure to Poison Joke.
When discussing a noun in English, we often use a possessive pronoun such as my or your to indicate ownership. However, such pronouns are relatively uncommon in Latin; ownership of something (or someone, for that matter) is generally conveyed through the use of the genitive noun case. Still, since we want a close translation, it's appropriate to use a pronoun here. As with regular nouns, pronouns need to have the same case, number, and gender as the noun(s) to which they refer (mannulus parvus), which gives us meus.
So, we have our first clause translated. Let's move on to the second.
The Latin word for friendship is amicitia, but while this might seem straightforward, it's worth noting that friendship in the ancient world was quite different from how we think about the concept today. In theory, it was considered the highest and purest bond that could exist between two men (with an unfortunate emphasis on men, and lack of consideration of women); Cicero attributes such qualities to it in his philosophical tract De Amicitia (On Friendship). In practice, though, amicitia often had a lot more to do with politics, and the complex set of social conventions and allegiances known as clientela (patronage). Still, let's take it at face value here. As with our first two nouns, it's nominative in case and singular in number; unlike them, it's feminine in gender.
Our one and only verb. Latin verbs have five key characteristics: person, number, tense, mood, and voice. Here, it's enough to say that we need est, the third person singular present indicative active form of the verb esse (to be). Were we to get this wrong, my old Latin professor would no doubt suddenly appear to wreak a terrible vengeance on us all.
As with the use of equus instead of mannulus, I've often seen the word magicus used for this part of the phrase (I've even done it myself a few times). Given that it's a cognate of magic (and neat evidence of how our English word has evolved), this is an easy mistake to make – but magicus is in fact the adjective form of the real word we want, magia. This is the difference between saying "friendship is magical" and "friendship is magic" – a key distinction in light of the show's themes. As with friendship, magic had a different meaning in the Roman world, mixing with religion and superstition in complicated and much-debated ways; for our purposes, we'll once again take the word at face value. And since we're comparing two nouns with est, we're again using the nominative case and singular number; the noun itself is masculine.
So, there you have it, right? Mannulus Parvus Meus: Amicitia Est Magia.
Well, not quite. One great advantage to an inflected language like Latin is that you don't have to rely on word order to convey the intended meaning. Take a simple English sentence like "I am throwing the ball". It follows a standard order: the subject (I), the verb (am throwing), and the direct object (the ball). We know that I'm the one doing the throwing because the personal pronoun is at the beginning of the sentence, and the noun is at the end; if I rearranged the sentence as "The ball is throwing I", it would not only be an example of poor grammar, but it would also paint a very different (albeit rather entertaining) mental image.
Now let's look at that same sentence in Latin. It can be directly translated as ego iacio pilam, but while technically accurate, this lacks real Latin style. We can already tell from the ending of iacio that the verb is in the first person – that I'm the one doing the throwing – which means we can do away with the ego altogether. More importantly, we know from the accusative ending of pilam (from pila, a first declension noun) what's being thrown, so the word needn't fall at the end of the sentence. Thus "I am throwing the ball" simply becomes pilam iacio, with no loss of meaning. Latin is nothing if not economical, and this flexibility in word order makes for some great poetry (and some hellish translation exercises).
And since we've gone through all this effort to get the words in correct Latin, we ought to follow the Latin word order, too. Our first clause is already looking good in the order we tackled it: we have the subject, then the adjective, then finally the pronoun. As for the second clause, let's move the verb Est to the end, to more closely follow Classical style.
Of course, if we really wanted to be sticklers, we'd also have to remember that punctuation marks like colons and printing conventions like spaces are modern artifices, not to mention that Latin had no u or lowercase letters in its alphabet – all of which would leave us with something like this:
But if we go down that road of pedantry, we'd probably also have to factor in the many abbreviations Romans used in their inscriptions, so let's leave in the spaces, the modern (and lowercase) letters, and the friendly colon, which finally gives us:
Mannulus Parvus Meus: Amicitia Magia Est
So, there you have it. Quite a lot of work for just six words, but hopefully you learned something. If you'd like to know more, there's a nifty Latin tutorial here, and if you can recommend any other handy resources, please do so in the comments.
Now, if you want something really tricky, try singing this new title to the theme tune.
♫ Mannulus Parvus Meus
I used to wonder what friendship could be... ♫