What does the error message non-static method <name> cannot be referenced from a static context mean?

The problem lies in understanding the meaning of static. The elements (attributes or methods) declared as static by means of the modifier staticcan be understood as elements that belong to the class and not to the class instance. In other words, static elements are global to the class that is loaded into memory. Here is an example of using a static method:

public class UnaClase {
    public static void log(String mensaje) {
        System.out.println("[LOG] " + mensaje);
    }
    public void logNoEstatico(String mensaje) {
        System.out.println("[LOG no estatico] " + mensaje);
    }
}

public class ClasePrincipal {
    public static void main(String[] args) {
        UnaClase unaClase = new UnaClase();
        unaClase.log("hola mundo"); //llamando a método estático desde instancia, es válido
        UnaClase.log("hola mundo"); //llamando a método estático directamente desde la clase, es válido porque el método estático le "pertenece" a la clase y no a las instancias

        unaClase.logNoEstatico("hola mundo"); //llamando a método no estático desde instancia, es válido
        //UnaClase.logNoEstatico("hola mundo"); //no se puede llamar al método no estático directamente desde la clase, no es válido
    }
}

Since these elements belong to the class and not to the instance, you cannot use instance elements to work with static elements. What does this mean? That a non-static attribute or method cannot be called from a static method. Let's review the method:

//el método limpiaCadena es estático, no necesita ninguna instancia
//de la clase para ser utilizado
public static String limpiaCadena(String s) {
    s = (s == null) ? "" : s.trim();
    //el método hazAlgo no es estático, entonces necesita
    //que se llame desde una instancia de la clase
    //como no existe una instancia aquí,
    //el compilador muestra el mensaje de error correspondiente
    hazAlgo(s);
}

How to solve the problem?

The simplest solution is to not use attributes and non-static methods directly inside static methods . This is simply a mistake. If you have a situation where you "need" to call a non-static attribute or method within a static method, I'm telling you that you're making a serious design mistake. Warning posted.

A "simple" solution is to change the non-static method to static, but you must understand the meaning of the change (if you don't understand the meaning, re-read from the beginning of the answer).

There are alternatives to this problem:

1. Create the class instance inside the static method:

   public static String limpiaCadena(String s) {
       s = (s == null) ? "" : s.trim();
       new Clase().hazAlgo(s);
   }
   

   Only use this if the class does not maintain state. However, this is a strange design and not recommended.

2. Declare the class as an argument to the static method:

   public static String limpiaCadena(String s, Clase instancia) {
       s = (s == null) ? "" : s.trim();
       instancia.hazAlgo(s);
   }
   

   This is a better alternative, cleaner in design but you will need more code.

Or just call the method like this:

new Clase().hazAlgo();

Taking your published code, it would be like this:

public class Clase {
    public void hazAlgo(String s) {
        /* implementación */
    }

    public static String limpiaCadena(String s) {
        s = (s == null) ? "" : s.trim();
        new Clase().hazAlgo(s);
    }
}

I think this might work too: https://docs.google.com/document/d/1oKikiQtWVeFpkrhLrSceermh54-K14oSOYp29WLCHXc/edit?usp=sharing

To put it in code instead of images it would be:

Before (with error)

public class test {

    private volatile int establishedChangingTimeInterval;

    public static void main(String[] args) throws InterruptedException {
        setTimeInterval(10);
        System.out.println(getTimeInterval());
    }

    public int getTimeInterval() {
        return establishedChangingTimeInterval;
    }

    private void setTimeInterval(int x) {
        establishedChangingTimeInterval = x;
    }

}

After (no error):

public class test {

    private volatile int establishedChangingTimeInterval;

    public static void main(String[] args) throws InterruptedException {
        //solution:
        test WeCanTakeItFromHere = new test();

        WeCanTakeItFromHere.setTimeInterval(10);
        System.out.println(WeCanTakeItFromHere.getTimeInterval());
    }

    public int getTimeInterval() {
        return establishedChangingTimeInterval;
    }

    private void setTimeInterval(int x) {
        establishedChangingTimeInterval = x;
    }

}