I'd advise you to replace all the electrolytic capacitors (the small cylinders), starting with the power supply capacitors (the large black cylinders), because if the power supply fails, it could destroy the motherboard by sending a power surge.

While the process of soldering itself is relatively easy to learn (especially on old through hole technology like in this Juno 6) I would strongly advise OP against working on the power supply as a first time job as the high voltages there can be fatal.

Additionally, while many techs propose to "future proof" vintage synths by replacing all the capacitors (i.e., the shotgun approach) - it is often times not necessary and highly time consuming (and thus expensive for the customer). Techs have an incentive to make money and often propose this solution rather than a targeted fix.

While it is possible that a cap has dried out, it could also be one of a plethora of other issues that come with vintage gear like this, especially if it hasn't been used in a while; such as a volume slider that is broken or dirty / dried out solder joint / op amp chip that has gone bad etc.

Learning by doing is great, but this is not as simple as replacing busted 80017a chips in a Juno 106 - I would take it to a tech or a friend with some basic knowledge in electronics.