Pudge depends on his abilities to deal damage, playing him as a solo on mid lane is a very good choice because he will take levels quickly and these will be helpful to gank. However, if you have an ally which combines well with Pudge, you can go with him on the safe lane (bot radiant, top dire).
Early game / (Level 1 - 6)
Just farm without taking any risk until level 3 (except if your opponent gives you the perfect occasion to kill him).
Once level 3, your Hook has a good range and you will maybe be able to try hooks from under your tower, or if you’re full life, you can attempt to go melee directly for your opponent to be at range of your Rot. When he’ll take the damage of Rot, his reflex will generally be to retreat far froms his creeps and it is exactly when you have to take the opportunity to follow him and hook him to kill him. Take care while approaching, be sure to don’t attack your enemy directly or the creeps will protect him and attack you, which could make you lose a lot of health at once.
Once you’re level 6, you can normally kill your opponent if you manage to succeed your Hok by just doing the Hook/Rot/Dismember basic combo.
On the safe lane:
Take position before the beginning of the game to have the vision on the rune spot, because making the first blood with Pudge is pretty easy if you have a good rune.
If you are lucky, you’ll maybe get an invisibility or haste rune, if not, leave it to your ally because he will be the one attacking the target while you slow it.
Hide behind the trees and surprise the enemies by coming from behind. The goal is that you use Rot to slow the opponents meanwhile your team mate attacks the target which you should kill wuickly. be careful though, there is a risk that you lose a lot of health doing this. If your enemies both have a stun or high damage skills at level, don’t do something silly!
One the lane, try to farm without taking too much harass and if you have an opportunity, Hook your target and kill it with the help of your mate. Always focus the enemy who has a control and the less HP first (Crystal Maiden for example is a perfect target).
Once you are level 6, you should be able to kill anybody on your lane pretty easily.
Mid-game / (Level 7 - 16)
Once you are level 7, you will have to move everywhere on the map to gank on other lanes. It’s the moment of the game where Pudge is the strongest because he can kill an enemy quickly. Ensure to be mobile and to always have a teleportation scroll to be able to help your allies.
Late-Game / (Level 16+)
During late game, Pudge is less effective because his damage are less of a problem for the enemies, so he will often become an engage/tank. If you manage to Hook an enemy before a teamfight, you will easily eliminate him with the help of your allies and before going in the fight 4v5.
During teamfights, try to use your ultimate on the enemy carry or on a hero that is especially annoying. Your goal is to deal damage with your Rot and to Hook the fugitives. Your placement during teamfights is capital so pay attention!