A number of things you can do with a rack of lamb but here is my favourite.
First of all, you need to trim your rack of lamb. In other words, the bones protruding from the meaty part, make sure they are clean of any fat.
Then:
Get a load of garlic and chop into 3/4 inch length sticks. Get some fresh rosemary and then with a thin sharp knife, prod into the fleshy part of the lamb and add the stick of garlic and a sprig of rosemary. Do this about 15-20 times, depending on the size of your lamb.
Then in a bowl, add some olive oil, salt, pepper and this time some crushed garlic. Mix together and then rub into the meat. Cover with clingfilm on a plate and put into a cool place, for an hour. If you can, ideally leave in the fridge for 24hours to get a good flavour going through the meat.
about 30 mins before cooking, take lamb out of fridge and allow it to sit (no handstands for this piece of lamb!) Lamb left to reach room temperature will cook more evenly.
Now you have 2 choices: This is the chef's way! Get a pan and put it on the stove and wait for it to be smoking hot - often professional kitchens will just use a metal tray. Then you want to sear your lamb. As it already has oil over it, no need to grease the pan. Just put your lamb straight into the pan and turn to a different section of the meat after about 1 and a half minutes. Ultimately, you're not looking to cook, just to brown the outside to keep the juices in.
Then take your meat and put into oven at 175C. Keep the juices from the pan - put on a high heat, add some red wine and a bit of flower and keep moving around in the pan - makes a lovely gravy/jus.
Alternatively, if you don't want to sear your meat, you can put it straight into the oven. For a lean piece of meat, pre-heat your oven to 230c and put your lamb in for about 15 minutes. Then turn down the temperature to 175C (this is when you would usually put the meat in the oven had you used the above searing method)
Lamb will take about 25 minutes per pound to reach medium-rare. For best results, try using a roasting rack, so heat can get underneath the meat. Alternatively, you can cut up 2 onions into half and put them so the lamb sits ontop of them - get the same results.
Once meat is cooked, cut into 2 bones pieces, serve with some mint sauce and a side of your gravy. Hopefully you've got some nice roast potatoes and veg to serve with as well.
Other alternatives include breadcrumbing, different spices, herbs etc - but I'm just a fan of garlic, rosemary and natural gravy (with red wine

)