Put In Order and Arrange

Put In Order
To put in order means to create an organizational pattern for something. You can put items in order by putting them where they belong or put an event in order by making specific plans. In this last sense, British people would use the phrase put on an event.
Ex: Because Mike was always a messy child, his mother decided to pay him £5 every time he put his clothes and books in order in his room. By May, his room was spotless and he had £200.

Ex: When Caroline found out her son was finally coming home from university, she put on a party in his honour. All his close friends and family were there to welcome him home.
When something is messy or disorganized, it is out of order. Usually in British English disarranged or in such disarray would be used instead. Also, a machine is out of order if it is broken or inoperable.
Ex: The clothes shop was in such disarray that it took over an hour for customers to find what they needed. The manager hired two new employees to help put things back in place.
Ex: Because the drinks machine was out of order, Josh had to drive all the way to the shop to get a drink for his lunch. For that reason, he was ten minutes late coming back to work.
Arrange
To arrange means to plan or organize an event or put items in a specific order. Therefore, you can arrange something like a party or tea with friends, or you can arrange your shoes in your closet.
Ex: To keep a clean working environment, Josh likes to arrange his tools in size order. He keeps smaller tools like nails and screws separated from larger tools like hammers and drills.
Ex: For Michelle's 16th birthday party, her sister worked hard to arrange a special brunch celebration. All Michelle's close friends from school were there in honour of her special day.
If you arrange items like flowers or candy in a specific way, it is called an arrangement. Flower arrangements and others are very popular gift items for holidays and birthdays.
Ex: One of the most costly items in many weddings are flower arrangements. Because flowers come in so many varieties, they make a colorful and attractive visual decoration.
Ex: Chris is not a big fan of cake, but he loves chocolate candies. For his birthday this year, I bought him a special arrangement of different chocolates instead of a birthday cake.