Map from Google - Shetland

In the Shetland Islands, situated to the north of Scotland, the climate is oceanic, cold and wet most of the year. The wind blows frequently, and can be stormy especially in autumn and winter. Summer is very cool.
Here are the average temperatures in Lerwick, the main town.
Average temperatures - Lerwick
LerwickJanFebMarAprMayJunJulAugSepOctNovDec
LerwickJFMAMJJASOND
Min (°C)1123589108632
Max (°C)556810131414121076

Rainfall amounts to about 1,250 millimetres per year; the rains are frequent throughout the year, but especially from October to March, while there is a relative minimum in spring and summer.
Here is the average precipitation in Lerwick.
Average precipitation - Lerwick
LerwickJanFebMarAprMayJunJulAugSepOctNovDecYear
LerwickJFMAMJJASONDY
Prec. (mm)14512012570556065851051401451451260
Days221920141111121317212122203

Winter is long and runs from mid-November to mid-April, and it is cold but not frosty: the average temperature is a few degrees above freezing. Wind and humidity, however, along with the lack of sunshine, exacerbate the sensation of cold. Given the latitude, the days are very short from November to January. Snowfalls are quite frequent, though not abundant. Cold winds of polar origin blow quite often, but for the presence of the sea the temperatures do not drop by much, so there are often light frosts, but the temperature rarely drops below -5 °C. Instead, during the period when the mild westerlies blow, the temperature remains a few degrees above freezing, and can even reach 8/10 °C, but the sky is cloudy, and wind and rain are frequent. Intense Atlantic depressions, which in this area occur often, can bring windstorms, and cause storm surges.

The short spring, from mid-April to late May, is cold: the temperature remains low, and returns of a more intense cold are possible, with some snow showers, even in the first half of May. But the days are long, the wind slows down a bit, and every so often you can see even the sun.

Summer, from June to August, is very cool, humid and rainy, and sometimes windy. Temperatures are similar to those of the Mediterranean coasts (Sicily, Cyprus etc.) in winter. When it goes well, daytime temperatures approach 20 °C, which might not even happen for a whole summer. But the days are very long, especially in June and the first half of July, when you can see the white nights. Summer is the least windy season, even though some days in which a strong wind blows are always possible.

Autumn, from September to mid-November, is cloudy, rainy and windy, and progressively colder.

The amount of sunshine in the Shetlands is mediocre all year round: cloudy skies are the norm. However, the (relatively) sunniest period goes from April to August.

Shetland

The sea is obviously cold all year round: at most the water temperature touches 12 °C from July to September.
Here are the average sea temperatures.
Sea temperature - Shetland
ShetlandJanFebMarAprMayJunJulAugSepOctNovDec
ShetlandJFMAMJJASOND
Sea (°C)888891012121211109

When to go

The best time to visit the Shetlands is the summer, from June to August, being the mildest season. However, you have to reckon with cloudy skies, wind, rain and a little cold at night.
In June, it's a bit colder than in July and August, but the days are very long (19 hours, compared with 18 in July and 15 August). In September, the temperature is similar to that of June, but it rains more often and the days are shorter (remember that in the 23rd of September, the autumnal equinox, the day lasts 12 hours everywhere in the world).