I want to make a vehicle that a player can ride in, shoot bullets with, and will auto jump one block. However, I have no clue where to start. Any ideas?

That's a lot all at once, I'd start with making the car and having it auto-jump one block.  Like the horse.

Try to make minecarts that don't require rails...

You can take a look at my mod JavalCars' source on GitHub. https://github.com/gegy1000/JavalCars It doesn't have any shooting, but it automatically goes up blocks and can drive around.

Try to make minecarts that don't require rails...

 

Unfortunately, the rails handle most of the Minecart movement logic.

Fairly easy start with

public class EntityVehicle extends EntityAnimal {

public EntityVehicle (World par1World) {
	super(par1World);
	this.setSize(1F, 1F);
}

public EntityVehicle (World par1World, double par2, double par4, double par6) {
	this(par1World);
	this.setPosition(par2, par4 + (double) this.yOffset, par6);

}

}

//then look at horse code for the rest in particular pay attention to

 

// this is my customized version for my Bicycle vehicle

@Override
public void moveEntityWithHeading(float moveStrafing, float moveForward) {
	if (this.riddenByEntity != null) {
		this.prevRotationYaw = this.rotationYaw = this.riddenByEntity.rotationYaw;
		this.rotationPitch = this.riddenByEntity.rotationPitch * 0.5F;
		this.setRotation(this.rotationYaw, this.rotationPitch);
		this.rotationYawHead = this.renderYawOffset = this.rotationYaw;
		moveStrafing = 0;	//moveStrafing = strafing. Should be 0, since we don't want the bike to move side to side.
		moveForward = ((EntityLivingBase) this.riddenByEntity).moveForward* bicycleMovementSpeedMultiplier;

		if (moveForward <= 0.0F) {
			moveForward *= 0.25F;	//you move 1/4 of the speed when going backwards

		}

		if(this.onGround){
			this.jumpPower = 0.0f;//(float)this.getBicycleJumpPower();
		}
		if (this.jumpPower > 0.0F && !this.isBicycleJumping() && this.onGround) {

			this.motionY = this.jumpPower;	//getBicycleJumpPower()

			this.onGround = false;
			this.isAirBorne = true;

			this.jumpPower = 0.0F;
		}

		this.stepHeight = 1.0F;
		this.jumpMovementFactor = this.getAIMoveSpeed() * 0.1F;

		if (!this.worldObj.isRemote) {
			this.setAIMoveSpeed((float) this.getEntityAttribute(
					SharedMonsterAttributes.movementSpeed)
					.getAttributeValue());
			//System.out.println("moveStrafing: "+moveStrafing+" moveForward: "+moveForward);
			super.moveEntityWithHeading(moveStrafing, moveForward);
		}

		if (this.onGround) {
			this.jumpPower = 0.0F;
			this.setBicycleJumping(false);
			//System.out.println("jumpPower: "+jumpPower+" if (this.onGround)");
		}

	} else {
		this.stepHeight = 0.5F;
		this.jumpMovementFactor = 0.02F;
		super.moveEntityWithHeading(moveStrafing, moveForward);
	}
}

 

and pay attention to

/**
 * Returns true if this entity should push and be pushed by other entities
 * when colliding.
 */
public boolean canBePushed() {
	return this.riddenByEntity == null;
}

/**
 * Called when the mob is falling. Calculates and applies fall damage.
 */
protected void fall(float par1) {
	if (par1 > 1.0F) {
		//this.playSound("mob.Horse.land", 0.4F, 1.0F);
	}

	int i = MathHelper.ceiling_float_int(par1 * 0.5F - 3.0F);

	if (i > 0) {

		this.attackEntityFrom(DamageSource.fall, (float)i);
		if (this.riddenByEntity != null){
                this.riddenByEntity.attackEntityFrom(DamageSource.fall, (float)i);
            }

		Block block = this.worldObj.getBlock(
				MathHelper.floor_double(this.posX),
				MathHelper.floor_double(this.posY - 0.2D
						- (double) this.prevRotationYaw),
						MathHelper.floor_double(this.posZ));

		if (block.getMaterial() != Material.air) {
			Block.SoundType soundtype = block.stepSound;
			this.worldObj.playSoundAtEntity(this,
					soundtype.getStepResourcePath(),
					soundtype.getVolume() * 0.5F,
					soundtype.getPitch() * 0.75F);
		}
	}
}


/**
 * Called when a player interacts with a mob. Here we mount the player on the vehicle when right clicked.
 */
public boolean interact(EntityPlayer par1EntityPlayer) {
}

public void onLivingUpdate() {
	super.onLivingUpdate();
}

public void onUpdate() {
	super.onUpdate();
}

@Override
public EntityAgeable createChild(EntityAgeable par1EntityAgeable) {
	return null;
}

@Override
public double getMountedYOffset(){
	return 1.0;
}
/*
 * Returns true if the new AI system should be used. Should not remove, otherwise the vehicle will use the 
 * AI of a passive mob 
 */
@Override
protected boolean isAIEnabled(){
        return true;
    }

@Override
public boolean isOnLadder() {
	return false;
}

also [joke alert] the Thank You Btn is located  over here somewhere -------------------------------------------------------------------------------------------------------------------------------------->

@Thornack, how do you mount your entity if the interact() method is blank?