Abuse cool downs. Almost every player in the lower leagues will use their abilities (oftentimes haphazardly) in lane. If you can time engages with those ability activations, you can win the fight.
Example case
vs
:
-As Volibear, keep an eye on how GP uses his Q. If he uses it to poke in lane, try to bait GP as deep as possible into your own minions, then turn around and Q him. Done correctly, you throw GP really deep into your minions, his Q already proc'ed minion aggro, and you won't have to worry that much about GP's minions. Assuming he didn't poke you down too hard leading up to that, you can guarantee a won trade in early levels. If GP uses his Q to farm, keep an eye on how close he gets to you and how close your own minions are. The moment he uses his Q on a minion, that's the time to attack him with your own Q. Done correctly, GP won't be able to shoot you in the following trade for an extended amount of time since he just burned the cool down on a minion.
-As GP, be aware of Volibear's W. Depending on how passively Volibear plays, you may be able to start fights the moment it wears down to guarantee the bear won't have his free attack speed. The few Volibear players who use his W to farm can also be taken advantage of this way. If Volibear wants to get into a fight, all of his power rests in his W. If you can keep an eye out for the rare moments Volibear will execute a minion, that's a prime time to fight. Aggressive Volibear players also tend to be tempted to shove the lane with their E abilities. Although that ability isn't as valuable near the mid game, it's an active you definitely want to keep an eye on early levels. Unfortunately, GP does not have the fight priority in this situation, as Volibear's engage potential is simultaneously faster and stronger in most contexts. You want to keep your range at all times possible, use your Q wisely (whether it's farming or poking), and be ready to react to Volibear's aggression.
Different champions have different tactics, but the general rule is to recognize what ability all of your opponent's strength is in, and fight them the moment they use it. GP tends to put all his points early on on his Q, so the general idea is to fight GP the moment he mistimes his Q, for example.
I HIGHLY recommend picking up a champion with hard engage - someone who can immediately leap onto the opponent and/or hard cc them - if you want to learn how to trade. They tend to be the best at abusing cool downs like this, compared to soft engage champions (champions who focus on poking down the enemy before fighting and only after maybe starting fights when optimal) like GP, who can't abuse cool downs as well.