Depends on the coin.
Usually, the easyest way is to download the wallet, open the debugconsole and type "setgenerate true". This being said, it's often also the slowest way
A different option is to edit the coin.conf file in your roaming profile (or the hidden folder if you're using linux):
server=1
rpcuser=USRNAME
rpcpassword=RANDOMPASSWORD
rpcallowip=127.0.0.1
rpcport=8332
then download mining software to connect to this server... Either using an asic, your GPU or your CPU
A thirth option would be to join a pool (if it exists) and follow the pool tutorial (if exists).
This is not true for 100% of the coins. Some can be mined this way, others cannot
