How do I start saving money from a young age to prepare for big purchases such as homes and cars?

You can earn or invest. Assuming investing can wait, you can focus on earning with different part time jobs eg. participate in research studies, work event jobs (like the Coffee Festival) or give tuition. If you really want to start investing perhaps you can work out an agreement with your parents!

Personally though, I think saving is much more important when growing up because young people like me really spend too much - peer pressure, indecision, whatever. Here are 3 areas I think you'd do well to focus on!

1. hanging out with friends: when you want to hangout but would be too broke for another cafe, consider dabaoing food to an open area like rooftops/open fields, sleepovers, cycling trips or even hike -- saves alot over time!
2. following (expensive) trends: trends will come and go - though you'd be tempted many times (like, I don't know, Fila Destroyers) but growing up is a great time to explore and figure out your own style and preferences, so others wouldn't decide it for you! You can explore styles by thrifting or clothes swapping with close friends for example.
3. trying to save too much: on the other extreme sometimes we spend lesser on important items - I'd recommend spending more on basics that can stretch for a longer period of time (eg. comfortable shoes, good quality basic clothing).