don't use electrical tape. It gets everything gunky, and when you go to replace the battery the next time it'll be a complete mess.
Anyways, the key to a good solder is heating up what you want it to stick too rather than the solder directly. However, if you heat just the metal you want it to stick to, you can overheat the components if they are too close. Do a tiny bit of preheating on the solder so you don't have to heat up the contact point for too long. Having a good iron is also really helpful. Find one with a nice point, rather than a blunt end as it makes it so much easier to get the heat where you want it.
other notes - for solder, you should probably use a 63/37 tin/lead solder as it has the lowest melting point (60/40 is pretty close) which should make it easier for you. Get one with a rosin flux as that is what is typically used for electronics.