When I use the serial interface built into the IDE, enter '10' and hit the Send button, it seems that the board is taking my input one character at a time. How can I make it see a ten and not a one and then a zero?
In my final product, I will have data coming to me one byte at a time, but it seems that right now inputs are being processed as one character = one byte, even when I'm sending in a number that's much less than one byte worth of data.
Also, slightly unrelated - it seems that Serial.available() just increments a number somewhere, so every time there is new data, it rises. Is this just the way the function call works, or do I need to be manually clearing the receive buffer even after a Serial.read() command?
As long as you're using the serial interface, you shouldn't be so surprised to discover that the data is sent and received serially. Interpreting a '1' followed by a '0' isn't part of sending and receiving - that's for you to do (or not do) in your programming.
Serial.available() reports on demand the number of characters that have been received. Serial.read() will deliver one received character for each call/request you make. Isn't that wonderful?
it seems that the board is taking my input one character at a time.
Yes that is how it works.
How can I make it see a ten and not a one and then a zero?
write code that gets the characters one at a time and accumulates them into a variable.
For each character multiply what you already have by 10 and add the new character value (value not ASCII data received ).
Do this until you see a LF or CR character.
it seems that Serial.available() just increments a number somewhere, so every time there is new data, it rises.
Yes and every time you do a serial read it decrements.
do I need to be manually clearing the receive buffer even after a Serial.read() command?
No once you have read all the characters this will drop to zero.
If you want to send a number 10 instead of a string with character 1 and 0, you can't do it on arduino serial monitor. Download a decent free serial monitor and you can do it on that monitor. I use Termite on windows.