July is smack-dab in the middle of Nepal's monsoon season, which means rain every day and generally warm temperatures. Along with August, this is when the Everest Region gets the highest rainfall of the year. But if you're prepared for wet conditions and understand that rain clouds may obscure your views, it's usually possible to trek to Everest Base Camp (EBC) in July.
The temperatures at Namche Bazaar are comfortable in July, with an average high of 60°F (16°C). The higher into the mountains you go, the cooler the temperatures and the lower the rainfall, and it will certainly rain at lower elevations. There's also a chance of landslides blocking trekking trails, and muddy paths. That said, even during monsoon, it generally doesn't rain all day every day.
Crowds & Costs
In early July you may still encounter some expeditions returning from EBC after climbing (or attempting to climb!) the peak. (Climbing season typically runs from May to June, with the arrival of the monsoon making conditions too difficult and dangerous). Otherwise, you're unlikely to encounter many other trekkers on the EBC trail in July. This is low-season. You won't struggle to find a bed in decent teahouses this month, although some will be shut for the season.
If you really want to trek all the way to EBC in July, you'll probably encounter the most rain at lower elevations (although nowhere in the Everest region is exactly 'low'); the higher you go, the less rain there will be. But, rain clouds are likely to obscure views everywhere, even when it's not raining. If you're willing to brave a few days of trekking in the rain, you may still be able to check out EBC itself in decent conditions.
Alternatively, exploring the Everest region without going all the way to EBC is a good option in July. Base yourself in Namche Bazaar and go for day hikes from there. If some days are a real washout, you can enjoy the cafes, shops, and even museums in the little Sherpa town. Namche Bazaar is two days' walk from Lukla.
What to Bring
Make sure to bring good waterproofs for trekking in July, and enough clothes that you don't have to re-wear the previous day's wet ones. Some people prefer an umbrella for when conditions are showery, though if it rains steadily, a comfortable rain coat and rain pants are a good idea.
Trekkers have polarized opinions about whether it's necessary to bring entertainment like books, e-readers, or playing cards on a Himalayan trek. In an ideal world, you'd be so absorbed in the spectacular views and trails that you won't need these distractions. But in July, your chances of being delayed or rained in are high. Bring that book.
Check out this handy guide to packing for a trek in the Himalaya: Trekking Gear List for Nepal.
Getting There & Away
The quickest and easiest way of getting to the Everest region in July (as well as every other month) is to fly from Kathmandu to Lukla. Be aware that flights are often delayed or canceled because of conditions in Kathmandu, Lukla, or en route. These chances are even higher in July. If flying to/from Lukla, leave yourself plenty of time to make important international connections, and bring some entertainment.
While you might be tempted to think that going overland is a way to avoid flight delays, this isn't recommended in July. Overland access to Lukla (such as the 'Pioneers' Route' from Jiri) is likely to be blocked by landslides on the roads.