How do i read forced checkmates like these ?

Game 1: lichess.org/analysis/r3k2r/5p2/2N2np1/qp1p4/2pPpP2/P3P3/2P1Q1PP/2K3NR_b_kq_-#1
Game 2: lichess.org/analysis/r1b3rk/2p4p/p2b2qP/1p1Pnp2/4n3/P3P2N/1PQBBP2/R2R2K1_w_-_-

Is there any specific method to read the game ahead ?
Or is it simple brute force ?

Do tactics, tons of tactics. You need to learn motifs. I would choose a hand selected tactics collection because this increases the learn effect.