This will probably be the first educational building you will plop. Utilise in a position that will increase the properity and happiness of a harder to reach residential area. Along with a new school, you can also add some school bus stops. The Grade school can be updated with more school buses and more classrooms. Perhaps you'll only need one grade school for your City until it becomes a considerable size, as there are other educational establishments which you can add such as High School, Community College and University.
Later in the game you'll have the opportunity to open a high school, usually after a department of education has been plopped in the Region. This allows you to educate a greater number of students with it's multiple classroom expansions and also add a Gymnasium which is useful for visitors to your City as well as residents.
Placed near to Industry, this will have a positive effect on the technical level of Industrial units located in proximity to it. So if you are interested in taking your industry down the tech route, such as producing processors and TVs (these are great salable commodites and can be also be used towards some Great Works projects) a Community College is an essential addition to your City later in the game.
The final and most costly educational establishment is the University. Add a University and it will have a positive effect on the tech level of your industry, as well as open up a plethora of improvement options in the form of faculties. For example add a faculty of Buisness to improve your the profits (and in turn your tax recipts) from commerce in your City. Add an engineering faculty to open up improvment options in Coal an Oil power plants.
The University can be expanded with Dormitories which sleep a 500 students per block.
You can also start costly and time consuming research projects such as a Solar Power Project to unlock an improvement the Solar Arrays, a powerful and less spacious alternative to the normal solar panels.
you also have the facility to add a library whenever you want, this has a positive effect on the education level of your sims and the general happiness of residents close to the library.
Upgrading your Education Service
A successful thriving City will soon find that it's education system is in high demand and you will get prompted to add additional classrooms to an existing school. Providing a good education service has positive effects on the wealth and happiness of your sims as well as on crime levels. The only problem in adding extra classrooms is that they usually mean knocking down an adjacent building, a residential block or something - however there are top floor classrooms which can be added later on. Once your school is packed to capacity you should really max out your school bus service for that school and make sure there are adequate school bus stops.
A maxed out grade school can be a funny shaped thing, so to maximize your plot space try plopping a park or two in the spare spaces created by the extra classrooms, as in the image below.
Filling Space Around a School with Parks
You could also add another school, either another grade school, or a high school. Personally, I'd go for a high school before adding a second grade school as there needs to be a good path through elementary education through to university - eventually. You can only add high schools if you have a Department of Education in the region.
At this point you should also ensure that you have adequate library facilities, if you have already plopped one, select it to see how useful it is being to your City and consider the possibility of adding a second.
As long as you have a Department of Education in the region you'll also have the option to open a Community College, these have a positive effect to adjacent industrial zones and will increase the tech levels of those industrial blocks close by. This is handy when it comes to progressing through to producing processors and TVs which are high profit items and can be sold to help fund your daily City expenses.
At some point early in the game you'll be prompted to start a school, if you don't have another City in the same region with an Education Government building, then the only option available to you will be Grade School (and a library). If you are focusing your City pureply on mining, then you may want to just omit Education from your plans, however, standard Cities should have a good Education system as it adds to the wealth of residents, the technical level of your industry and like in life, is generally all good in terms of benefits. Education can be a costly expense however so be careful what you add.