Can someone explain rib grafts, diced cartilage, and fascia to me?

The simple answer to your question is that if you have a virgin nose or one that has not been worked on before, then the best option is to use the cartilage that is already present in your nose, for example septum. Most primary rhinoplasties can easily be performed with the cartilage that is already present in the nose. The major exception being for people with congenitally small noses that need major lengthening. Often in revision surgery, you need to obtain cartilage from elsewhere, such as the ear or rib. Whenever tissue from other parts of the body are required there is always the risk of irregularities, firmness, displacement, resorption, etc. That being said the choice of tissue used elsewhere depends upon whether it is replacing structure or just being used as onlay material for augmentation. If support is required and a large amount of cartilage is required then whole rib is best. If camoflauge or just correcting depressions and non structural areas are being corrected, then ear cartilage is sufficient. Diced cartilage for augmenting the bridge of the nose is often used when there are concerns that a large amount of augmentation of the bridge is required and you want to soften the firmness that is often felt with rib cartilage. This is often a preference of some but not all surgeons. Fascia is just to keep the graft material in place or to act as a barrier to prevent you from seeing or feeling irregularities.The length of duration of effect is the same for all of the material except for fascia which typically is resorbed by the body over time. 

All of the techniques can give lasting results. Each has its indications and also limitations. A rib graft is for major reconstructive defects and it has a higher complication rate. It also requires more extensive surgery to harvest a portion of your rib.
Diced cartilage can be an excellent graft material, harvested from your cartilaginous septum or from your ear (concha...the buccal portion). It can provide a smooth contour over the dorsum of the nose, as it can be "crushed" into very fine particles to be placed over the dorsum to create volume but also to smooth the appearance. Cartilage can also be placed at the tip of the nose to give more projection. 
Fascia can be harvested from many sites and placed over the dorsum. It can be used alone to give the smooth look and feel...it can also be used to wrap around the crushed cartilage. Each has its own pros and cons. Good luck! 

The source of cartilage is dependent on the degree of augmentation and projection you are trying to achieve.  A significant change can be created using cartilage from your septum and your ears; however, to achieve maximum augmentation and refinement, rib cartilage is necessary.
The reason rib cartilage provides a greater degree of refinement is because it provides more structure since it is stronger.  Greater augmentation (or building of the bridge) is also possible because there is more cartilage available from the rib.  In addition, for projecting, lengthening, or counter-rotating the tip of the nose, rib cartilage grafts are often necessary to provide long-lasting results.
Consulting with a rhinoplasty specialist who does a high volume of rhinoplasties using rib cartilage will give you the best option regarding your exact nose.    

Material used for grafting during rhinoplasty is chosen depending on the amount needed and the purpose for the graft.  When a large amount of structural support is needed, particularly in reconstruction, rib cartilage is used because large blocks can be harvested. This material can warp over time and, as with any graft, can shift position if not properly secured.  Rib cartilage harvest leaves a chest scar and has the potential complication of a collapsed lung caused during harvest.When less material is needed ear cartilage is used.  This is a common practice, has little to no morbidity, and is a mainstay for rhinoplasty operations, both cosmetic and reconstructive.  Septal cartilage is also commonly used, but this can be more difficult to harvest and has some additional, though minor, risks, especially in inexperienced hands.Fascia is used when there is need for bulk without support.  Diced cartilage can also be used for this.  Both fascia and diced cartilage can shift or resorb but in general both methods are safe and effective.For best results be sure to consult a surgeon certified by the American Board of Plastic Surgery who has a good deal of experience with grafting and rhinoplasty. A thorough review of his/her portfolio of pre- and post-op pictures should give you an idea of the results that are reasonable to expect.