How to encrypt plain message with RSA
The straight-forward way to do this is:


Convert the ASCII string into an array of bytes.
Convert that byte array into a large integer. For that you need a library with support for arbitrary large integers (e.g. BigInteger)
Endianness does not matter for this.
For encryption, the library should already offer some modular exponentiation method, because otherwise you will have to write square-and-multiply yourself, where you apply the modulus after every step.
Decryption is the same as encryption, it's just modular exponentiation again.


Of course this is just for this basic exercise. In an actuall application, you definately need:


A proper padding scheme, e.g. RSA-OAEP
You usually don't encrypt the message directly. Instead, hybrid encryption is used in all cases, so that it doesn't matter how long the message is.
Follow the standards, e.g. PKC#1, section 4 for the data conversion from integers to byte strings (thanks to @MaartenBodewes for pointing that out)
And to be honest: You should just use an implementation of RSA (and other encryption schemes) provided by a cryptographic library.