Ok...well in that case you have three options depending on which level of detail you want to go into. In increasing order of complexity:
1. The hobbyist way: wire together some pre-build modules readily available from hobby electronics companies like Adafruit: http://www.adafruit.com/products/390
This is the method engineers would use to quickly prototype circuits to test certain aspects of an early-stage product, or to produce a quick proof-of-concept. This is also great for hobbyists who want to quickly built up a project without necessarily having to learn all the ins-and-outs of the circuits they're using, or the principles behind them. This is the approach I would recommend to you if you're just interested in getting started building some simple projects.
2. The electrical systems design way: source a 5V output DC/DC boost IC, and a single cell lithium-ion charge IC, and simply build up the recommended circuits, hit up your preferred chip supplier and search for DC/DC boost chips, and li-ion charger chips; things like the LT1303
(actually don't use the LT1303 this was just an example, I used this before several years ago, there are better, cheaper, chips out there now) etc.
This is the method engineers would use to design functional circuits for use in consumer, commercial, and industrial goods and applications; where the aim is to produce a low-cost integrated system a part of a larger product. This method requires knowing or learning some of the principles behind circuit design (particularly with high-frequency DC/DC boost circuits which require at least some consideration of the circuit layout to avoid instability or ringing). And is what I would recommend to you if you're looking for a project that'll teach you how to build circuits.
3. The low-level electronics engineering way: build your own DC/DC boost and regulation circuit for 5V output, and your own DC/DC buck circuit with CC/CV control for the charger. Stuff like implementing DC boot circuits
, and dealing with charge profiles
This is the method engineers would use to build highly custom circuits that are needed when pre-fabricated ICs are not sufficient. This is also excellent for learning about the field of power electronics, and DC/DC boost circuits and battery charging. This is the approach I would recommend to you if you're looking to learn more about power circuits, and control loops.