You can grow cucumbers without a greenhouse but these are poor things by comparison with varieties grown under cover. Outdoor or ridge cucumbers are spiny and stumpy whilst indoor ones are smooth skinned, long and gently curved. Both originated long ago in India with the greenhouse strains selected and improved in China and Japan. The greenhouse cucumbers of the past were a fickle crop but now are as easy as courgettes. Indeed few vegetables have been improved as much.
The greenhouse cucumber was once prone to many diseases, needed daily inspection and removal of all male flowers as pollination would make the fruits bitter, and they required hotter conditions. Most modern cucumbers are resistant to many of the old disease problems. Better still they’re usually all female (so no male flowers and no daily inspections). There are also varieties bred to be small fruited; these carry more fruits sooner and replace them more quickly- just one plant will give you a fruit, often two or three, every day throughout summer.
Seed sown right now (January) will, in most years, be cropping in late March or April and in full production for the following five months. The seed is expensive but worth it as the returns are so good. Ideally sow seeds singly in small pots of sowing compost (some believe it’s better to sow the seeds on edge and not laid down flat). Keep the compost just moist not wet and in a warm light place when the seedlings will soon emerge.
The seedlings must be kept frost free and preferably warm but most of all they crave maximum light. The roots soon fill the pots so then move them on into bigger pots of potting compost. Never bury the neck of the seedling where it emerged from the compost as it will surely rot, set the root-ball slightly protruding from the new compost.
As growth progresses a large tub, bucket sized or bigger, will be best, the plant effectively standing proud on a hill of compost and so remaining dry round the neck. The plants run into vines which can be left unpruned to ramble or be trained along strings or canes. The compost must be kept moist but never waterlogged with warm water containing a dilute liquid feed (fish waste emulsion is revolting but good).
You may wish to foliar feed with seaweed sprays as well as cucumbers respond to regular feeding. Humid air is better than too dry as the latter encourages red spider mites which are controlled by regular misting or with the commercially available predator Phytoseuilis which you simply release onto the plants.
Hot bright summer days (we can wish) may scorch the foliage so some light shading may be necessary. Otherwise there’s only one trick to watch for- if production of new fruits suddenly slows or stops then search assiduously because for sure there is a hidden fruit getting big, fat and yellow; find it and remove it at once!