I have a 4/2 Spiked Baloth (with trample) and my opponent has an untapped 1/1 Bird with flying. He has only 2 lives and I want to finish him off. Can I attack directly even though my attacker doesn't have reach or flying (and his creature does)?
Yes, you can attack your opponent with your Spiked Baloth, and you will win if you do so. (Trample is relevant; it's the reason you win in this scenario.)
However, your question seems to indicate that you don't understand exactly how combat works. Combat goes in step:
In the Declare Attackers Step, you say what creatures are attacking which players. You can only attack players, and it doesn't matter what creatures they have to block. In your particular case, you would declare the Spiked Baloth as an attacker attacking your opponent.
In the Declare Blockers Step, your opponent says which of their creatures are blocking which of your creatures. This is where the flying becomes important. When they're blocking, the fact that the bird has flying just means that it can block your creature even if your creature has flying. In this particular situation, your opponent would declare that their bird is blocking your Baloth.
In the Combat Damage Step, all of the combat damage is dealt at the same time. Since your Baloth has trample, it only has to deal as much damage as the bird's toughness (1) to the bird, and it can deal the rest (3) to your opponent. The bird just deals 1 damage to your Baloth. Then your opponent would lose because they have -1 life.
In addition, flying and reach only affect what attackers a creature can block. They don't affect damage, or what creatures can attack.
As the attacker, you don't have to worry about what creatures the defender has. You attack a player, and that defending player gets to choose if and how to block.
Reach only matters on a blocking creature. It means that the creature may block other creatures who have flying. It is not relevant in this case.
Flying creatures cannot be blocked by creatures without flying or reach. There are no restrictions on what a creature with flying can block. That means that flying is also not relevant in this case.
This means that, if you attack in this case, your opponent may choose to block with his flying creature. If he doesn't, he will lose since you deal 4 damage to him. If he does, he will still lose, since your creature will deal 1 damage to the blocking bird, and 3 trample damage to the defending player, which is enough to bring his life to 0.
You can and, if you attack, you MUST attack the player. In Magic, you always (with exceptions in planeswalkers and multiplayer games) attack the player. It is the defensive player who CHOOSE if he will block or not.
Let's say the opponent has 5 lives. It is your attack phase and you attack (in a 1vs1 game, you don't even choose who to attack, you just Attack the opponent player). He can decide to block your creature with his 1/1 flier (losing it and getting 3 damages himself) or just let the damage go through, getting the 4 damages and keeping his creature alive.
In the actual state of the game the trample MATTERS, because he will die because of the 3 trample damage points. Without trample, he could just block with the flier and stay alive in 2 lives.