How do I prepare for the Language Aptitude Test (LAT) when it isn't a language that I can learn?

The LAT can be quite intimidating given that it's a made up language which seems nothing like the language you're studying at school. However, like all languages, the made-up one has rules which you can work out in order to understand the basics and translate what is necessary. Honestly, the LAT can be quite fun if you like puzzles (and languages of course!)
The most useful way to prepare for the LAT is to do the past papers, of which there are copies readily available online. Doing it timed is also essential given the (unfortunately) relatively short time allowed in the exam. It's important to make LOTS of notes on the page, both when preparing and in the exam itself - as soon as you notice a grammar rule/vocab word, write it down! This saves having to go back and re-decipher a word later on in the test, as words are pretty strange-looking and therefore not very memorable. Additionally, if you run out of time in the test to write down an answer properly, your notes will still be there which I presume will be useful to the examiner - they want to see how you think!
I found that 'coding' words was very helpful for quickly deciphering the words - for example I would underline the subject of the sentence, circle the verb and draw a box around the object. This is especially useful if the word order of the 'language' isn't fixed (which it quite often isn't). Use the example sentences to find similarities between phrases which can then be used to work out specific vocabulary words. Pay attention to the way in which the same word may differ slightly depending on whether it's the subject or object of the sentence; it's worth looking over/learning a bit about cases if you don't study a language which requires them.