You can read the official documentation, I just make it easier here.
Pull the image from Dockerhub or GHCR:
podman pull docker.io/searxng/searxng:latest
# ghcr.io/searxng/searxng
and run it in the background:
podman run -d -it -p 4005:8080 -name searxng searxng:latest
Create a subdomain and get a certificate for it then point it to the port.
server {
	listen 80;
	listen [::]:80;
	server_name sx.urdomain.com;
	location / {
		proxy_pass http://127.0.0.1:4005/;
		proxy_buffering off;
		proxy_set_header Host $host;
		proxy_set_header X-Real-IP $remote_addr;
	}
	listen 443 ssl;
	ssl_certificate /etc/letsencrypt/live/sx.urdomain.com/fullchain.pem;
	ssl_certificate_key /etc/letsencrypt/live/sx.urdomain.com/privkey.pem;
	include /etc/letsencrypt/options-ssl-nginx.conf;
	ssl_dhparam /etc/letsencrypt/ssl-dhparams.pem;
}