Weather & Temperature
Understanding Systems
Mountain Thunderstorms - Their Formation and some Field-Forecasting Guidelines by Jim Bishop is a short read and will help you understand how a storm is building. Practical Mountain Weather by John Papineau gets into more detail into how weather forms in the mountains, including wind patterns etc. Mountain Weather by John Renner similarly has a large section on how weather in mountains generally works, and is then followed by regional examples in North America.
It's highly recommended to have a basic understanding of how weather works. Similar to reading the mountain, not just maps, it helps to be able to read the sky.
Directionality of systems is very important. Monsoons are now coming up to the Sierra during El Nino years (boo). Checking forecasts in specific areas in previous years when one was approaching could show around 2" a day in SE SEKI, but only 0.1" up in central Yosemite or Emigrant. Likewise atmospheric rivers / pineapple express will hit the westside first and should be a little lighter by the time they hit the crest.
Microclimates are also very important to consider. I've been camped in a duffy patch under a little raised patch of trees in a large meadow and woken up to a frozen frost covered meadow but a drier and warmer immediate area just from tree cover and being 5-10 feet above where cold air settles, likewise camping a bit above a lake is noticeably warmer. On day four of a trip I encountered an hour of heavy hail that covered the route from W. Pinnacles Basin to Three Island Lake. Inches accumulated in spots, making the trip up and over Peak 11,840+ treacherous, Three Island Lake itself and all surrounding peaks were untouched, It'd be reasonable to assume the much higher and nearby peaks of Seven Gables or Turret Peak would have snagged the precip, but nope. No forecast will tell you that.
Forecasts
Weather.gov
Weather.gov is the most popular resource used for the weather in Sierra (it runs on the NOAA model). You click on a specific location on their map to get a forecast for that specific spot - it's useful to test a few passes and altitudes for longer trips. Look for named features or reference a Topo map to make sure you're clicking on the right place. Doing a search for "weather gov AREANAME", replacing area name with a park or wilderness area etc can get you started closer on the map. There is no web app, but there is a mobile version of the website. I find weather.gov can sometimes be a bit pessimistic on precipitation (indicating there will be more than actually happens), but planning for that is safer than the opposite!
There is a section below "Detailed Forecast" called "Additional Forecasts and Information". Within that section click on "Forecast Discussion" to see written notes about the weather coming up and possible impacts. Having a narrative understanding of what is going on is often more useful than a if this or that service expects an area to have slightly more or less rain or a few degrees difference in temperature.
If you're using an iPhone, someone helpfully shared a widget you can tap to load your GPS coordinates on weather.gov. Useful for when you're on a peak or pass and get signal after being offline for a while. :)
If you want to get really nerdy SpotWX lets you choose from different NOAA models (what weather.gov runs on).
Mountain Forecast
Mountain forecast is the second most popular choice - some people say it runs a bit cold up at higher altitudes.
Topo mapping clients
Gaia and Caltopo also provide weather forecast map layers as a topo layer. This blog post goes over how to use both.
Other
I personally use Carrot on my phone as I can check a few different models easily, and have a grandfathered cheap plan for Weatherstrip which is a neat visual way of showing NOAA forecasts.
Windy has a nice map view of thunderstorm predictions fairly far out. Obviously accuracy at the tail end will be somewhat low, but it can be useful to visualize where a storm is coming from and maybe flip a loop to be low when it hits the worst etc.
Open Summit has a great UI in their dedicated mobile apps - detailed two day forecasts for free, five day forecasts for $20 a month. Seems great for peakbagging, of less use for longer backpacking trips, but if you're already subscribed to Open Snow why not?
Understanding Forecasts
Different forecast models produce different results - they will never be 100% accurate, but for frontcountry use Forecast Advisor is useful as they will show historical accuracy of various weather services matched against local weather stations. For the Eastern Sierra this is less useful (Mammoth Lakes shows Bishop information) and weather in the mountains is even harder to predict. It's worth noting that while Accuweather usually does well in the frontcountry, it doesn't take into account elevation or other changes to terrain necessary and is fairly worthless for deep backcountry.
I generally like to look at a few different models to get an idea of a range of outcomes. Knowing whether the uncertainty centers around the where the storm is expected to go or how strong it will be can be useful. The precise estimates for rainfall etc are essentially the most likely outcome of a model run multiple times based on known conditions information that are fed into historical outcomes from similar conditions.