Arduino Uno cannot write to LCD-09395 serial display

This is my first post, so please have patience.
I bought a new Arduino Uno and a serial display LCD-09395 from Sparkfun.
Three wires connect the devices: GND, +5v, and Arduino Tx to LCD Rx.
I use a library named LCD03, but cannot get a Hello World program to run
correctly, On upload, sometimes nonsense characters appear on the LCD,
sometimes nothing appears.

Google searches have not found me an example of a 3-wire connection.

Has anyone successfully used this hardware? What library did you use and
from where did you get it? Did you have to set the baud rate or is using the
default 9600 adequate; I do not need superfast transmission.
Could you send me or post a working Hello World program?

Thanks in advance,
JoeC

Have you looked at SparkFun's page on the display? There are code examples about halfway down the page.

https://learn.sparkfun.com/tutorials/pic-based-serial-enabled-character-lcd-hookup-guide

They use the SoftwareSerial library.