What's your technique for the differences in sentence structure order?

Couldn’t think of a catchy title.

Basically, the order of words in Japanese is different from English a lot of the time. For example, “a room with a big bed” would be: 大きなベッドのある部屋. Where, if we are literally translating the words, they’re in the reverse order. i.e., in English the room is mentioned first, then the bed, whereas in Japanese it’s the opposite.
Also for things like: “A person looking for a dog” becomes 犬を探している人, where the word order in something akin to “Dog, looked for by a person”.

Do you fine fellas have a technique for remembering these differences? I’ve been trying to simply brute force these example sentences, but I can’t seem to get out of ‘english-order-mode’, if that makes sense.

I think its only really one difference

In English, extra information comes after the relevant noun. In Japanese, it comes before.

I never really used any technique, it just came with time and practice.