Hey there!
I've had a few rabbits in my life and they've always been outside.
The first had a hutch and we put her in there at night, then give her free run of the garden - which was huge - all day, only when we were out there though. She would also come inside a lot too. I was very young - about 10 - when my parents got her so I don't really remember too much, except she did escape once and we lost her for a night which was terrifying and so upsetting. But she loved the garden, the neighbours dog would come over to investigate - unknown to us - but I did catch her chasing him out the garden once. However, I wouldn't keep a rabbit like this now.
My second rabbit again had a hutch in a shed and he stayed in there at night, he had free run of the garden as well, this one much smaller, and only when we were in the house, whenever we left the house we put him in a large wire run with a wire lid so nothing could get in.
The rabbit I currently have actually sleeps on my terrace - I live in an apartment with a small terrace. She basically owns the terrace, it's safe and completely walled in. She also has a big bunny house out there that she loves (
http://www.auntyanimal.me.uk/BunnyHutch.jpg), a parasol for when it gets hot, and an area she has chosen as her bathroom, our door opens out to the terrace so we leave this open during the day, when we are in or out and she has free roaming of the apartment living area and her terrace. At night we shut the door and she stays outside.
I don't really remember any specific things we did the introduce them to the outside. I think with the current rabbit we just opened the door and she was out enjoying the smells and sounds. I do think it's important for them to have somewhere sheltered where they can hide from hot or wet weather and anything that may startle them.
I would get a rabbit hutch with run, place it outside then introduce your bunny to it, stay outside whilst he/she gets acquainted and once they start relaxing and playing you can leave them, come out regularly and check on them, especially if you're worried about predators. But the run and house should protect them from any dangers should something creep into your garden. Something like this:
http://www.bunnybasics.net/images/jasmine-hutch.jpg
When you're out I'd probably leave bun inside and not in the run - especially if weather is unpredictable and you'll be out for a while. This is why we leave our apartment door open so ours can come in and cool off when she wants.
Mine is a very confident, brave and inquisitive bunny so she will explore everything and poke her nose anywhere, I feel this is because she feels safe in her environment. So just keep an eye out for any tell tale signs of stress and you should be fine.
Hope this helps!