What method should I use to plan what clothing to pack for destination X?

In addtion to specific weather and social aspects, a general approach to deal with temperature is layering, as detailed on onebag.com, one of my favourite travel sites.

The basic idea is that you adapt to changing temperature by adding or removing layers of clothes. Accessories can be helpful as well: an umbrella protects both from the rain and from the sun.

In addition to the weather, you need to also consider social and cultural norms. For example, you may be obliged to keep your knees covered in a place that is warm enough for shorts, or need to cover your head when normally you don’t. You may be going to restaurants that demand men wear ties, or forbid beach shoes.

To investigate these norms, a suggestion from an answer to a similar question is to look for pictures of tourists in the area you’re considering. That’s a start. I have found wikivoyage entries detailed and useful. Take a look at these:

… dress modestly and appropriately. While Fiji is a tropical country, beach-wear should be confined to the beach. Take your cues from the locals as to what they consider appropriate dress for the occasion. When visiting towns and villages, you should be sure to cover your shoulders and wear shorts or sulus (sarongs) that cover your knees (both genders). This is especially true for visiting a church, although locals will often lend you a sulu for a church visit. There is no nudist/naturalist or topless bathing in Fiji.

• Fiji (the Respect section)

When visiting any holy site or religious neighborhood one should dress modestly. For men this means long pants, a closed shirt with sleeves, and a head covering. For women, it means a skirt that falls below the knee, a shirt with elbow-length sleeves and no exposed cleavage or stomach. This applies to churches, mosques, and synagogues, as well as the Temple Mount (Noble Sanctuary) and Western Wall (the plaza by the Wall is essentially an open-air synagogue, and there are mosques on the Temple Mount). When in religious neighborhoods as well, such as Mea Shearim, it is advisable to follow these guidelines.

• Jerusalem (in the Stay Safe section)

For most tourists, dressing for daily sightseeing in Japan puts you at a disadvantage: you will most likely stand out, no matter how you dress, next to the throngs of salarymen (male office workers) and gradeschoolers in uniforms. Japan is known for being very fashionable, whether dressing in kimono, tailored suits, or the latest trends from Harajuku. First and foremost: wear shoes that can easily slip off and on, and keep a pair of socks handy as needed. Athletic shoes are acceptable, but keep them tied loosely so you can slip them off and on. Quality walking sandals (not flip-flops) and dress shoes are acceptable as well. Japanese culture sees shoes as being dirty, and before entering someone’s house, certain restaurants, dressing rooms, and temples (to name a few), you must remove your shoes. The older generation of Japanese tend to group steps into two types: wooden (“clean”) and concrete or stone (“dirty”). If you are going to be stepping on to wood, take your shoes off and place them to the side; there might even be a cubby hole for you to put your shoes in.

• Japan (the first paragraphs of the Dress section, it goes on for pages)

You may also want to email the hotel where you’re staying to ask about dress code in specific restaurants, or ask here for specific cultural (as opposed to general climate) considerations.

TL;DR
Use weatherspark to find the time-of-year that weather in your hometown corresponds to the weather at the time and place you’ll be visiting.

Compare Historical Data with a Place You Know

It used to be a real pain to try to figure out how the weather was likely to be at a new-to-me destination at some future time. In the last few years, however, I have increasingly found weather websites that properly consolidate historical weather data into a usable form. My favorite of such sites is weatherspark.com. I’m not affiliated with weatherspark in any way, I just find their representation of historical weather data to be the most useful for travel.

Suppose I’m planning a trip to Reykjavik in July. I would go to the weatherspark page for Reykjavik, Iceland.

Temperature

The first thing I determine is the temperature ranges to expect for July. I do this by looking at these two temperature graphs:

Temperature Chart

Hourly Temperature Bands

From this, I can tell that for my trip in July I will most likely encounter temperatures of between 10 and 15°C during daytime hours. I used both charts to arrive at this conclusion.

You’ll want to go to the weatherspark page and read the legend below each of those graphs. It might take a few minutes of studying to understand how to interpret them, but it is well worth learning how. Now that I understand how to read the graphs it takes me only about 30 seconds to evaluate the temperature for any destination with weatherspark.

Once I know what temperatures to expect in Reykjavik, I go to the weatherspark page for where I live and find the time of year with temperatures around 10 to 15°C. It turns out that mid-May and late September in Vancouver have similar temperatures to July in Reykjavik. So, I basically pack clothes that I would expect to wear at home in mid-May and late-September.

If there isn’t overlap between your hometown’s weather and you destination, I find that it also works well to look at weatherspark pages for other destinations on similar latitudes that I have visited in the past.

Wind, Precipitation, and UV

Heavy wind, precipitation, and high UV index are secondary factors I consider when packing. Weatherspark has good wind and precipitation data. I usually have to do some googling for UV index. I use the same method to select clothes for wind, precipitation, and UV as I do for temperature: Find comparable wind, precipitation, and UV conditions for a time-of-year and place I know well.

Consider the Activities You Need to Pack For

For packing purposes, I find it useful to split my activities into three categories: Formal (i.e. dining out), activewear (i.e. getting sweaty), and casual (i.e. everything else). This is particularly useful when I have multiple destinations with different weather and different activities planned for each. For one long trip with many different weather types and a few formal events I actually used a spreadsheet to count days of each combination of weather and category. It was totally geeky, but worth it because of the lighter baggage and less laundry I had to do while traveling.