Completely agree with Bruno. Flux and nice hot soldering iron.
Word of caution about shorting capacitors: they can store very large voltages and you could possibly do harm to yourself or other electronic components on the board. Before shorting anything, test with a voltage tester to see if there is charge. Better idea is to disconnect from power for 24hrs before beginning the process. IMO, anything above 10V and you are asking for trouble if you short it out.
When soldering in new capacitors, make sure the polarity (+ or -) is correct. Very important.
Most important to match is the capacity, more or less is usually bad - if you are really stuck for parts, find something within 10% of the original value. Voltage can be the same or higher, but never lower - lower will blow the new capacitor. As far as diameter is concerned, most replacement capacitors you buy are of better quality than the components used on the assembly lines, so the diameter can be slightly larger than the OEM you are going to remove; you should check, however, that the pins slide in easily without bending.