I don’t have a personal experience using Maicoin yet, therefore I’ll only be talking about the former one.
They seem to offer the same kind of services though so I'm sure the purchasing method is similar. Let me know if you've tried it.
Go to FamilyMart
The most straightforward way to get Bitcoin is to go to any FamilyMart store (around 3000 all over the place) and head straight to FamiPort. It’s an ATM-like machine where you can buy all kinds of transportation and venue tickets and much more.
Don’t even bother asking cashiers, the chances are they have no fucking clue what Bitcoin is.
Note that FamiPort is all Chinese but the process is easy as every option has a corresponding picture next to it. If I could do it, you can too.
#1 Tap the “Dollar sign” logo saying “繳費” which means “Payment”.
#2 Select the “Pencil and paper” logo with label “虛擬帳號” that stands for “Virtual account”.
#3 Type in “BTC” into the input field and confirm tapping on the blue button saying “確認" right next to it.
#4 Type in your (or your friends') Taiwanese phone number and confirm with the big blue button. This number is where you receive your SMS with instructions.
#5 Choose a temporary password to be able to send your soon-to-be-bought Bitcoins to your own wallet.
#6 Type in your desired amount of Bitcoins you want to buy. There’s a flat service fee of NT$25 that goes to FamilyMart.
#7 A summary screen will pop out. Make sure everything’s correct and tap the second blue button saying “列印繳費單” which means “Print the bill”.
After you finished all necessary steps the machine will print out the bill for you.
Just go to the cashier, hand over the bill and pay with cash or card - whatever you prefer.
You will receive an SMS in a couple of minutes with a link to a Bitoex deposit page.
You can either send Bitcoins to your own wallet or you can send it to your existing Bitoex wallet (you can also create one in the process).
Since everything’s in Chinese I would only recommend sending Bitcoins to Bitoex if you already have an account registered.
We will stick with the easier option - sending Bitcoins to your own mobile/PC/web/hardware/whatever wallet.
Send Bitcoin to your wallet
I would strongly advise you to do this step on your computer because it’s much easier to copy & paste your wallet address.
#1 Click the link in the SMS and tap the gray button saying “Other wallets”.
After the transaction is made you will be charged the network fee of 0.0005BTC which is currently around NT$5.
#2 In the next step, type in the password that you set up on the FamiPort machine.
Order number should already be pre-filled. Do it yourself in case it's not.
#3 Copy & paste your wallet address.
#4 Check that everything’s correct and confirm the transaction.
Your Bitcoins will be sent to the wallet specified in no time. Usually, it takes 10 minutes to confirm the transaction, but you should see it unconfirmed in your wallet almost instantly.