How do I pass variables between stages in a declarative Jenkins pipeline?

If you want to use a file (since a script is the thing generating the value you need), you could use readFile as seen below. If not, use sh with the script option as seen below:

// Define a groovy local variable, myVar.
// A global variable without the def, like myVar = 'initial_value',
// was required for me in older versions of jenkins. Your mileage
// may vary. Defining the variable here maybe adds a bit of clarity,
// showing that it is intended to be used across multiple stages.
def myVar = 'initial_value'

pipeline {
  agent { label 'docker' }
  stages {
    stage('one') {
      steps {
        echo "1.1. ${myVar}" // prints '1.1. initial_value'
        sh 'echo hotness > myfile.txt'
        script {
          // OPTION 1: set variable by reading from file.
          // FYI, trim removes leading and trailing whitespace from the string
          myVar = readFile('myfile.txt').trim()
        }
        echo "1.2. ${myVar}" // prints '1.2. hotness'
      }
    }
    stage('two') {
      steps {
        echo "2.1 ${myVar}" // prints '2.1. hotness'
        sh "echo 2.2. sh ${myVar}, Sergio" // prints '2.2. sh hotness, Sergio'
      }
    }
    // this stage is skipped due to the when expression, so nothing is printed
    stage('three') {
      when {
        expression { myVar != 'hotness' }
      }
      steps {
        echo "three: ${myVar}"
      }
    }
  }
}

Simply:

  pipeline {
        parameters {
            string(name: 'custom_var', defaultValue: '')
        }

        stage("make param global") {
             steps {
               tmp_param =  sh (script: 'most amazing shell command', returnStdout: true).trim()
               env.custom_var = tmp_param
              }
        }
        stage("test if param was saved") {
            steps {
              echo "${env.custom_var}"
            }
        }
  }

I had a similar problem as I wanted one specific pipeline to provide variables and many other ones using it to get this variables.

I created a my-set-env-variables pipeline

script
{
    env.my_dev_version = "0.0.4-SNAPSHOT"
    env.my_qa_version  = "0.0.4-SNAPSHOT"
    env.my_pp_version  = "0.0.2"
    env.my_prd_version = "0.0.2"
    echo " My versions  [DEV:${env.my_dev_version}] [QA:${env.my_qa_version}] [PP:${env.my_pp_version}] [PRD:${env.my_prd_version}]"
}

I can reuse these variables in a another pipeline my-set-env-variables-test

script 
{
    env.dev_version = "NOT DEFINED DEV"
    env.qa_version  = "NOT DEFINED QA"
    env.pp_version  = "NOT DEFINED PP"
    env.prd_version = "NOT DEFINED PRD"
}

stage('inject variables') {

    echo "PRE DEV version = ${env.dev_version}"
    script 
    {
       def variables = build job: 'my-set-env-variables'
       def vars = variables.getBuildVariables()
      //println "found variables" + vars
      env.dev_version = vars.my_dev_version
      env.qa_version  = vars.my_qa_version
      env.pp_version  = vars.my_pp_version
      env.prd_version = vars.my_prd_version
    }
}

stage('next job') {
    echo "NEXT JOB DEV version = ${env.dev_version}"
    echo "NEXT JOB QA version = ${env.qa_version}"
    echo "NEXT JOB PP version = ${env.pp_version}"
    echo "NEXT JOB PRD version = ${env.prd_version}"

}