The tools may be needed for manually soldering components to printed circuit board (PCB) are illustrated below (there might also be some other approaches available, such as hot plate, hot air, hot oven, etc.):
1.Solder station with a 25W to 30W soldering iron.
It would be good to have at least two soldering iron for re-work purpose. For instance, to de-solder some SMD components with two pads, such as: SMD resistor chips, SMD capacitor, and some SOIC chips, it would be fairly easy to use two solder iron heating both side of the pads at the same time for fast components removing. To de-soldering some TQFP chips, it would be good to have four soldering irons for rework purpose.
You can get solder irons and solder station from local stores such as: Wal-Mart store, Sears, Radio Shack, Ocean State Job Lot, etc. Some decent solder iron with station (such as a Weller WESD51) may cost as high as a few hundreds US dollars. For Do It Yourself purpose, you can find a good solder iron with station in a price range of 4 to 10 US dollars at local stores.
If price is not an issue, an temperature adjustable solder iron is recommended.
Fine points, 4.5" long, anti-magnetic Tweezers are highly recommended for SMD components handling. For instance, some resistors and capacitors are in a 0805 type of package, a tweezers will help a lot for pick them up and put them on the right position for soldering.
Tweezers are available at various local stores, also you can find them on online stores, such as ebay, Allied Electronics, etc.
A 2x to 10x magnifier is used to inspect circuits. A full inspection of the circuit board is highly recommended after all components are assembled and the circuit board is cleaned. The magnifier can let you have a good visual-inspection on possible flux residual, solder short-circuit or open circuit issue before the power supply is connect to the circuits. Magnifiers are available at various hobby store or hand-craft department of giant retail stores. Also some online retailers such as Jameco carry some decent portable magnifiers.
A 25 AWG or finer solder with flux core is highly recommended. Kester has a full family of solder for traditional and lead-free application. For Do It Yourself fans, a solder wire with water-soluble flux core is highly recommend for easy clean purpose. Solders can be ordered through local store like Radio Shack or online store like DigiKey, etc.
5.Liquid flux (solder paste) and brush
Liquid flux and solder paste can help the solder forming a quick and smooth joint with PCB pads.
A brush can help distribute the liquid flux to PCB pads or components pins. Water-soluble liquid flux is recommended for easy clean purpose. A Kester water soluble 2331-zx flux pen will meet most do it yourself requirement, and is available through many online stores like Digikey.
6.Residual cleaning tool
After the circuit board is fully assembled, all flux residual must be cleaned. An used toothbrush can serve this purpose very well.
So, save your used toothbrush and enjoy the process and happiness of Do It Yourself (DIY).