Hey Vindicat,
Basically in Logic you can layer many effects one on top of another. This is done using the Channel Strip which should be on the left of your screen. You'll see a heading saying inserts and then below it a load of rectangular boxes. By clicking and holding these boxes you can select an effect to add to the chain of effects. There may already be ones on there, you can click and hold on them to select a different kind of effect.
To edit the parameters of an individual effect, there are two things you can do. Either double click on it to bring up the controller for the effect, and edit settings manual. Looks confusing doesn't it, but its fun and rewarding to play around with!
But here's the handy bit - there are lots of built in presets for each effect which affect the parameters of them. Simply click on one of the effects in the channel strip, and on the right of the screen you have the Library. You are presented with a whole range of presets to choose from and experiment with.
Now here's the even more handy bit! Above the Inserts section of the Channel Strip, you will see another rectangle like the ones you use to put the effects in. Click on this, then go to the Library on the right, and you will see a plethora of presets. These presets allow you to choose a preset with a whole chain of different effects already done for you. This is kind of like what you get in GarageBand.
So for example, if you're recording a male singer, you could try clicking on the top box in the Channel Strip, then in the Library choosing Voice > Male Voice > Male Creamy Lead Vocal. This will automatically add a new chain of effects (Channel EQ, Compressor, Stereo Delay and Ensemble) to the Inserts. You can then go and tinker with the individual parameters of each kind of effect in the preset chain.
I hope that helps. And sorry if it was confusing/patronising in any places as I don't know what level of experience you're coming from. I'm not an expert but have lots of fun in Logic Studio!