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