Map from Google - Tenerife

In Tenerife, the largest of the Canary Islands, the climate is subtropical oceanic on the coast, that is, very mild and sunny most of the year, with little rainfall concentrated in the period from October to March. In inland areas, however, the climate varies with altitude and slope exposure. In fact, the slopes exposed to the northeast trade winds receive a fair amount of rain and are green, while in the rest of the island rainfall is scarce, usually below 250 millimetres per year on the coasts, but often below 150 mm, and this explains the dryness of the landscape on coasts and southern slopes.
The prevailing winds, the trade winds, make the northern side more humid, while tempering the heat along the coast during the summer; the trade winds blow with greater intensity in the middle of the day and in the afternoon, and are often moderate or even quite strong.
The days of Calima, characterized by abnormal heat and light wind, dominated by warm air masses from Africa, are relatively rare, and are most common in spring and summer, in practice these are the only days when the temperature exceeds 30 °C, and when the heat is unpleasant. The stifling heat is felt also on the hills, and often even more than in the plains, because hot air is lighter and tends to rise, while the coasts may remain tempered by the coolness coming from the sea.
The amount of sunshine on the coasts of Tenerife is good even in the winter months, and is great in summer, when clear skies are the norm. In inland areas, instead, on the north-facing slopes, mists and cloud banks may form with some frequency.

Tenerife, sea and Teide in the background

In the main town, Santa Cruz de Tenerife, daytime temperatures are very mild in winter, with highs around 21 °C in January and February, and warm in summer, with highs around 28/29 °C from July in September. Here are the average temperatures of Santa Cruz:
Average temperatures - Santa Cruz
Santa CruzJanFebMarAprMayJunJulAugSepOctNovDec
Santa CruzJFMAMJJASOND
Min (°C)151516161819212121201816
Max (°C)212122222426282928262422

The rain pattern is Mediterranean, which means that the bulk of the rain falls in autumn and winter, because these are the seasons when the Canaries can be reached by some Atlantic depressions, while in summer, it practically never rains. The total quantity of the rain that falls in a year is low: just 270 mm, therefore at a semi-desert level. Also in autumn and winter, weeks can pass without a raindrop falling, but sometimes there may be heavier rains, associated with flooding, as happened in March 2002, December 2013 and October 2014. Here is the average precipitation.
Average precipitation - Santa Cruz
Santa CruzJanFebMarAprMayJunJulAugSepOctNovDecYear
Santa CruzJFMAMJJASONDY
Prec. (mm)4035301551003305060269
Days54321100136632

Santa Cruz overlooks the sea, but there are neighbourhoods that climb the inland slopes, and along the road to San Cristobal de La Laguna you find a progressively cooler and humid weather. When looking for meteorological data of Tenerife, you often find those of the airport of La Laguna, which is the airport of the northern part of the island (called Tenerife Norte), and which is sometimes presented generically as "Tenerife", but being located at 600 metres, it has significantly cooler temperatures: highs are on average around 16 °C in winter, and 24/25 °C in summer. Here are the average temperatures:
Average temperatures - La Laguna
La LagunaJanFebMarAprMayJunJulAugSepOctNovDec
La LagunaJFMAMJJASOND
Min (°C)101011111213161616151311
Max (°C)161617181922242525221917

Lying on the northern slope, La Laguna is also more humid and rainy: rainfall amounts to 605 mm per year, with a maximum from November to January, of 90/110 mm per month, distributed in 8/9 days per month, but even in March and October it's about 60/65 mm per month: it is a very cool and moist microclimate, to be in the Canaries. In summer, however, here too there is little rain. Here is the average precipitation.
Average precipitation - La Laguna
La LagunaJanFebMarAprMayJunJulAugSepOctNovDecYear
La LagunaJFMAMJJASONDY
Prec. (mm)907565402010551560115105605
Days87864311378965

La Laguna, moist area of Tenerife

To the south of La Laguna, the northern slopes of Tenerife above 1,000 metres are even wetter and are covered by forests. Green areas and covered by forests are also found in the municipality of La Orotava, on the north side of Mount Teide, between 1,000 and 1,800 metres, where the trade winds are felt most. Above this altitude, however, rainfall becomes scarcer and the vegetation becomes sparser.
The Teide observatory of Izaña is located at 2,400 metres above sea level: at this altitude the winter is cold, so that the average temperatures from December to February are about 4/5 °C; in addition, at this altitude sometimes it can snow. Summer is mild, with temperatures not so high, but the tropical sun, especially at high altitudes, is very strong. Unlike on the coasts, here in September the temperature begins to decrease. Here are the average temperatures.
Average temperatures - Teide observ.
Teide observ.JanFebMarAprMayJunJulAugSepOctNovDec
Teide observ.JFMAMJJASOND
Min (°C)112359131410742
Max (°C)78911141823221814118

In the observatory, 435 mm of rain or snow fall, concentrated from November to March, while in summer the rains are sporadic.
Here is the average precipitation.
Average precipitation - Teide observ.
Teide observ.JanFebMarAprMayJunJulAugSepOctNovDecYear
Teide observ.JFMAMJJASONDY
Prec. (mm)856565251510215355075435
Days54431000234632

At higher altitudes, there is a mountain dry vegetation, as well as lunar landscapes and rocky deserts. Mount Teide is a volcano, 3,718 metres high. There is a cable car, the Mt. Teide Cable Car, which leads up to 3,550 metres: to get it you must book in advance.

Teide Observatory of Izana

On the southern coast, where there are places like Playa de Los Cristianos, Playa de las Américas, Costa del Silencio, we find the other airport of the island, Tenerife Sur. Here the temperatures are similar to those of Santa Cruz and the rest of the coasts of the Canary Islands.
Here are the average temperatures.
Average temperatures - Tenerife Sur
Tenerife SurJanFebMarAprMayJunJulAugSepOctNovDec
Tenerife SurJFMAMJJASOND
Min (°C)141415161618192121191816
Max (°C)212122222324262727262422

The rains are very scarce, amounting to less than 150 mm per year, therefore at desert levels, and are concentrated, as usual, in the cold half of the year. Here is the average precipitation.
Average precipitation - Tenerife Sur
Tenerife SurJanFebMarAprMayJunJulAugSepOctNovDecYear
Tenerife SurJFMAMJJASONDY
Prec. (mm)172015710014122630133
Days22210000122416

Tenerife south from above

The sea in Tenerife is quite cold in winter, even though not prohibitively, and stays cool in summer, as the island is located at a low latitude, almost to the Tropic, but in an area of the Atlantic Ocean where a cold current flows. Those who live in the island are accustomed to swimming even in winter, which also Nordic tourists do, or those who do not fear the cold. However, the sea temperature ranges from 19 °C in the period from January to April, to 23 °C in August, September and October.
Here are the average sea temperatures.
Sea temperature - Tenerife
TenerifeJanFebMarAprMayJunJulAugSepOctNovDec
TenerifeJFMAMJJASOND
Sea (°C)191919192021222323232220

When to go

For the sun and the sea, the best time is from May to mid-October. In the first period (May-June), the air temperature is a bit lower and the sea is a bit colder, but the days are slightly longer. In the Canaries, in summer the days are shorter than in Europe (while in winter they are longer), but due to the time zone adopted, the sun sets late enough.
To visit cities and make excursions to inland areas, you can choose April, May and the first half of October.
In winter you will appreciate the mild temperatures and you can often sunbathe, although we can not exclude a few days of bad weather. If you want, you can combine a morning excursion on Mount Teide, in search of the snow, with an afternoon on the beach.

What to pack

In winter: light clothes for the day, sweater and jacket for the evening, possibly a raincoat or umbrella. To climb Mount Teide, down jacket, hat, gloves, hiking boots.
In summer: summer clothes, but also a scarf for the wind, a light sweatshirt, a light jacket for the evening and windy afternoons; comfortable shoes for hiking. To climb Mount Teide, hiking shoes, sweatshirt and jacket for the highest altitudes.