'Cucumbers are sweeter when planted with sunflowers', that's what I kept hearing. I could find no scientific validity to this old wives tale so I decided to try it for myself a few years back. Lo and behold I'll be darned if it didn't work. Perhaps it was coincidence, perhaps just the placebo effect but my cukes certainly did taste sweeter. So come the next season I did it again, in a different section of the garden and once again I got what I believed to be sweeter cucumbers.
The sunflower should be started first, at least a week ahead of the cukes, as it will act as a trellis for the young cucumber vines. I wouldn't trust the sunflower by itself to support a vine full of rapidly growing cucumbers, some additional supports are advisable. The sunflower however is just dandy for supporting young cucumber vines.
The sunflower acts as a natural trellis for the cucumber vines. Plant the sunflower shortly before the cucumbers, about a week. Sunflowers grow very quickly, they can reach a foot in height within a few weeks. When you plant the cucumbers near sunflowers, use seedlings not seeds. The sunflower will mature long before the cukes, leaving the cucumbers a full grown sunflower to climb up. Some sunflower plants are gigundous and may need staking to prevent them from toppling over.
I would also have additional support for the cucumbers in place as the sunflower will not always support the full weight of a cucumber vine laden with rapidly ripening cucumbers.
Some varieties of sunflowers are slightly alleopathic, meaning that they emit compounds - phytotoxins which inhibit the growth of nearby plants. This doesn't seem to be of a major concern for cucumbers and curcubits as the advantages far out weigh any minor disadvantages. There is minimal evidence that sunflowers stunt cucumber growth. They do however inhibit seed germination, which is why the cukes you plant around sunflowers should be transplanted seedlings not seeds.
So far as the sweeter cucumbers - I'm scratching my head on that one. I like to add some valid scientific rationale to claims about companion planting that I publish. There are so many urban legends and old wives tale in that sector that it is hard to separate the wheat from the chaff - but for whatever reason cucumbers are sweeter when planted with sunflowers.