This is one of the must-know Rook and Pawn endgame. This is called the Lucena Position.
White to move. What is the plan?
The lucena endgame.............. 1.Re3+ Kd7
1.Re3+ Kd72.Re4 Rg23.Kf7 Rf2+4.Kg6 Rb25.g8=Q Rg2+6.Kf7 Rf2+7.Kg7 Rg2+8.Kf8 Rxg89.Kxg8
7.Rg5 White stops the rook
It is important to note that the hard work is done at this point- white wins with every single move except the trivial Rh3 (draws) and Rf1 (loses). Equally efficient here would be 1.Rf4 followed by 2.Re4+.
Yancey Ward 1. Re3+ (cutting Black King off) Kd7, 2. Re4! (ready for the Lucena Bridge) Rf2, 3. Kh7 Rh2+, 4. Kg6 Rg2+, 5. Kf6 Rf3+, 6. Kg5! Rg2+, 7. Rg4 and White wins