You want a pencil type soldering iron and rosin cored solder. Radio Shack, Sears, or most any hardware store should have what You need. I prefer to melt a little solder on the tip to tin it, then melt a little drop that will hang on the tip. Apply the iron tip with the drop to the conection, and when the solder flows remove the iron. this works if You don't have really fine solder. When it cools the repair is done. An alternate method is to put the tip on the work and apply the solder [sparingly] to the tip/work junction. This works best with really fine solder. Soldering paste like plumbers use is a risky option. Most are corosive and can cause problems down the road. Acid core solder is a NO NO for electrical work of any kind.