Hydricity? Energy storage? What are some of the ideas for storing energy generated by solar power?

Solar energy generates electricity when light is around. Unfortunately, there isn't much light at night. Consequently, other forms of energy need to be used during these times--or, energy captured during the day would need to be stored.

Source: Microsoft Clipart

The most commonly discussed storage method involves batteries. There are many well-established battery technologies that can be used immediately. However, these existing technologies are expensive. Utility-scale batteries are being researched in an attempt to lower costs and raise capacity. This is the tactic that Elon Musk of Tesla Motors has taken. Tesla lowered the cost of utility-scale storage to ~$250/kWh.

Even within battery technologies, there are a variety of options, some more in development than others. Elon Musk and many other companies use lithium-ion batteries. Lithium-ion batteries are currently the market leaders. For off-grid and some utility applications, people often use lead acid batteries (basically, souped up car batteries) due to their low cost. Flow or sodium sulfur batteries may be used on utility scales. Sodium sulfur batteries require higher temperatures for operation. These technologies are promising due to their cost, energy density, and lifetime.

There are other technologies out there that might offer more significant cost benefits down the road. For solar thermal power, one might combine solar thermal power generation with hydrogen generation and use the hydrogen as a storage medium. This hydrogen can then be used for industrial uses, turned back into electricity using fuel cells,  and/or used for transportation purposes.

We hear solar energy mentioned when climate change is discussed. How do we know how how solar fits into this?

Solar energy, itself, does not release greenhouse gases (although the energy required to make solar panels, themselves, often does--the precise "cleanness" depends on the specific technology, but modern technologies are cleaner than the status quo). At the same time, they absorb energy and pump it other places in the form of electricity (and, ideally, don't reflect much back to space). Consequently, solar panels change the energy distribution in their immediate vicinity. Computer models are used to predict the effects of solar cells on their local environment. Aixue He et al. recently published a paper discussing these effects. This paper was then picked up by the Washington Post. Solar panels, themselves, lower temperatures in their immediate vicinity. They absorb energy from their surrounding and convert it to electricity, which is sent into cities and towns. Those areas, then, use the electricity, often in ways that release more heat, resulting in warming of urban areas. It is important to note that these temperature increases are much less than those predicted without the use of solar or other clean energy sources.

It is important to note that precipitation is also affected by air temperature. Cold air can't hold as much moisture. If deserts are colder, they are often drier. Solar panels, where they are set up, decrease the local temperature, which A. He et al.'s study suggests would slightly reduce cloudiness and precipitation. It only takes a 2 C temperature decrease to reduce precipitation by 20 % in desert regions. For these reasons, it was found that placing solar panels in a mixture of urban and desert regions minimizes many of the local environmental impacts of solar cells.

The moral of the story is that no matter what you do, the environment is effected. It is just a question of degrees and in what way things are affected. 

What is graduate school like? How is it different from other schooling?

Graduate school is like no other beast. In the sciences, you both do research and take classes. When you start out, you are mostly taking classes but, as you progress, you do more and more research with fewer to no classes. By the time you graduate, there is little difference between being a graduate student and being a postdoc or research scientist. It is a transition and learning period. By the end, you are the world expert on the topic of your research. Answers are not in the back of a textbook or online. You make your own questions.