widget.cpp
/////////
#include "widget.h"
#include "ui_widget.h"
#include <iostream>
#include <cstdlib>

Widget::Widget(QWidget *parent)
    : QWidget(parent)
    , ui(new Ui::Widget)
{
    ui->setupUi(this);
    connect(ui->pushButton, SIGNAL(clicked(bool)),this,  SLOT(showWords()) );
}

Widget::~Widget()
{
    delete ui;
}

void Widget::showWords()
{
    QString words[] = {"пословица1", "пословица2", "пословица3"};
    ui->label->setText(words[rand()/3]);
}

////////
main.cpp
////////
#include "widget.h"

#include <QApplication>

int main(int argc, char *argv[])
{
    QApplication a(argc, argv);
    Widget w;
    w.show();

    return a.exec();
}