Certs and keys are in /etc/letsencrypt/live/
Point the webserver directly to the cert and key in the live folder, since it is updated during renewal. For example in a node.js app:
"keyfile": "/etc/letsencrypt/live/<domain>/privkey.pem",
"certfile": "/etc/letsencrypt/live/<domain>/cert.pem",
Or, for example in apache2:
SSLCertificateFile /etc/letsencrypt/live/<domain>/cert.pem
SSLCertificateChainFile /etc/letsencrypt/live/<domain>/chain.pem
SSLCertificateKeyFile /etc/letsencrypt/live/<domain>/privkey.pem