The most important causes of raspberry success are careful selection of plant types, a solid trellising system, and ongoing care that matches the plant type. If this is provided, your plant will reward you with decades of high fruit yield and a lot of satisfaction.
The techniques illustrated here are for the a classical everbearing variety called 'Summit'. Ideally, you should ask your local greenhouse what plant is more suited for your climate zone, and you should also ask for rooted canes that are certified as disease-free.
I chose an everbearing type because it will produce more fruit: if you nurture it well it's going to provide you with lots and lots of raspberries for cakes, gifts for your neighbors, packs of frozen berries and whatnot.
Summer-bearing varieties only fruit for about a month, and then it's all over. Everbearing varieties fruit around July, while summer-bearing begin production a few weeks earlier.
If you're trying to add variety to your garden you could consider adding a summer-bearing variety such as Brandywine, or even some yellow raspberries such as the "Golden" or "Fall Gold" and "Golden Harvest".
Raspberry plants are extremely prolific, and even planting a single cane will almost guarantee you will have dozens in a couple of years.
As for space, I suggest a two-tow strawberry patch 9 feet wide and at least 20 feet long. Allow 4 to 6 feet between tows as that will provide you enough space for picking fruits comfortably.
Raspberry plants tend to suffer from root rot, and they are gross feeders. A good idea would be to build a raised bed (about 20 inches high is enough), filled with 4/5 garden topsoil plus 1/5 sand, manure and peat. Raspberries prefer slightly acidic pHs of around 6. An ideal period to do this is around spring, so you will be ready to plant in spring.
Of course you can also plant raspberries directly in your garden, but be sure that you have a deep soil that drains well, or the plants will die to root rot.
Also, try not to grow your raspberries in a place where you previously grew tomatoes, potatoes and peppers, since it will increase the risk of your plant wilting to verticillium.
The best time to plant raspberry bushes is in early spring, well through summer (for summer-planting you will need a very healthy plant though). If you plant them in spring, you will often get the first fruits in summer!
Bare-root plants are to be soaked in a half strength solution of vitamin B1 growth stimulant (1/2 teaspoon per quart water), for six hours. After that, plant immediately (certainly don't leave them in the solution for more than a day, and don't wait too long to plant them or they'll die quickly).
After this, dig a 1-foot-deep, 1-foot-wide hole, put in some well-rotted manure and organic fertilizer, or 4-20-20 and mulch to retain moisture.
Plants should be set 3 to 5 feet apart, and mulch shouldn't be more than 3 inches deep Dig a hole 1 foot deep and wide per plant. In our case, we set the plants 3 feet apart in the row. Put a handful each of rotted manure and fertilizer in the hole. Add some water, pop the plant in, then carefully tuck the soil around and over its spread roots to make a small depression or basin at the surface, a place for rainfall to accumulate. Sprinkle some more rotted manure in this depression to provide a jump start for growth, then cover the ground around the plants with your mulch -- no more than 3 inches deep. We laid landscape cloth over our path between the rows and covered it with wood chips. Drip irrigation is the ideal way to water raspberries, and this is the easiest time to install it.
If all goes well, your raspberry plants will produce so much fruit that they will need external support to avoid falling over: a t-bar trelly is the ideal instrument to provide this support cheaply and effectively.
Bury a 6-foot post 1 foot in the ground, then fasten 30-inch crossbars with sturdy screws across the top and middle of each post. Add two tiers of wire, one 2 feet off the ground and the other stretched from the ends of each crossbar (a 16-gauge wire will do).
The purpose of pruning is removing the old, unproductive canes to make room for younger, healthier ones. Some of your new canes will start fruiting at their top in late summer, through fall. Wait until spring, keeping track of these canes, and prune these 1-year-old canes.
You should only cut them to just below the fruiting area (about level with the top support wire), as this will let them fruit in July, while new primocanes will grow rapidly from between the old canes.
These primocanes will fruit in late summer, and should be then thinned and their suckers cleared away (unless you want your entire garden filled with raspberries!).
In the second year, 2-year-old canes should be completely removed to make room for new ones (i.e. cut them at ground level), while 1-year-old canes should be trimmed as described before. Applying some well-rotted manure in early spring will ensure more production.
A good rule for keeping your raspberry plants healthy is to keep them damp in summer and dry in winter: mulching extensively is useful for keeping moisture to a good level, and remember that a drip system is the best way to water them.
Raspberry plants also need a lot of nitrogen to grow to full size (about 7 feet). Many growers use a lot of nitrogen, but I believe it's best to stop it around fruiting time: too much nitrogen will encourage the plants to produce leaves, but you want them to produce fruit instead!
Although raspberries are usually very sturdy and do not get many diseases, they can still be attacked by aphids, fruit worms and nematodes. Another danger is posed by maggots, who girdle the emerging canes and break them off at soil level.
Raspberries are self pollinating, but will need the aid of bees or other insects to self-pollinate, so try to find a spot with a beehive in the vicinity.
Other diseases you may encounter are root rot (very common if you overwater), fruit rot and spur blight. Fruit rot can be solved by picking fruit frequently in wet weather, and pruning the bush a bit.
Root rot manifests itself with the plant dying after flowering, at the first sign of warm weather.
Spur blight's symptoms are brown stains on primocanes, from midsummer to fall, during weather with high levels of humidity. The best "cure" here is prevention, which can be achieved with a lime-sulphur solution applied as a dormant spray.