Get Processing from processing.org. Download, extract, and launch. On Linux, just click the processing file.

Processing requires that either OpenJDK or Java to be installed.

Processing requires a void setup() function, which is a function that Processing expects whenever an application is launched. If you don't have a setup function, your application still launches, but with basic Processing defaults. Try this to start with:

void setup() {
    size(480,720);
}

Click the Run button in the top left corner to launch your [very simple] application: an empty window that is 480 pixels wide and 720 pixels tall.

Draw a rectangle on your canvas by invoking Processing's void draw() function:

void draw() {
    rect(10,10,80,80);
}

Click the Run button in the top left corner to launch your application.

Add some colour to your rectangle:

void draw() {
    fill(8,120,90);
    rect(10,10,80,80);
}

Click the Run button in the top left corner to launch your application.

Make a simple painting app:

void setup() {
    size(480,720);
}

void draw() {
    if (mousePressed) {
        fill(20,120,90);
        ellipse(mouseX,mouseY,25,25);
    } else {
        fill(random(10,120),random(10,80),random(20,200));
    }
}

More Processing tricks: you can export your application as a standalone Java app, or as an Android .apk as long as you have the Android SDK installed.

Processing's documentation is excellent. It has examples for all functions, with pictures.