My husband and I recently went on our Honeymoon and we absolutely loved it. We spent 3 nights in Hong Kong and 1 night in Macau, from this short time we learnt some awesome tips for getting around on the cheap. I have provided links that fully describe how each works, have a read of them, I'm sure you'll find them very helpful. Here's our top 7 tips:
1. Get an
Airport Card as soon as you arrive. For only HKD$220/AUD$27 we got a one trip card which included 3 days free travel anywhere in the northern territories. We only got the one trip card as we were not returning to the same airport and instead flew out in Macau. But if you're flying out from Hong Kong, get the two trip one. It makes travel so much cheaper, faster and easier. The MTR (standing for "Mass Transit Railway") is basically made up of lines, and is very easy to follow.

This is what an airport card looks like, make sure you get the right colored card
2. Grab an
MTR Map from the information desk, great chance to grab tons of other brochures to shop around for the best tour deals
3. From Kowloon Station, take a
Free Hotel Shuttle. It's easy to find, firstly ask for hotel shuttles, and you will find it in the K area in Kowloon or the H area in the Hong Kong Station. It really saves a lot of time, money and hassle. If your hotel isn't listed, try to research nearby hotels. Our hotel, the Kimberley was right across from another major hotel on the list so we got off at the same stop.

The Free Hotel Shuttle bus from Kowloon dropped as off at our hotel (near the Luxe Manor)
4. Have a go on the
Double Decker Buses. We absolutely loved sitting upstairs right up front, such a great experience, especially at night.

Sorry it's not the best photo, but it shows how massive the front window upstairs is, now that's what I call widescreen viewing!
5. Try the
Peak Trams. Part of the great tourist experience offered at Peak Tower, riding the peak trams is great fun. If you have an
octopus card, you don't need to buy extra tickets.
6. If you ever want to take a
Taxi, try to avoid it for longer trips especially when arriving or departing the country. Bringing luggage with you will cost an extra $5HKD per piece. It's still relatively cheap for short trips and will get you places faster that are nearby.
7. The nearest port to depart from
Tsim Sha Tsui to Macau, is the China Ferry Terminal. When you get to Macau make sure to avail of the Free Hotel Shuttles waiting just outside the terminal.

The Cotai Ferry is super fast and super comfortable to ride