Gewiss is an adjective that suggests a fixed, but not precisely mentioned (not necessarily unknown) amount of something. The amount is not necessarily large; it is typically above average or more than nothing and indicates that there is an amount (as opposed to nothing) or that the amount is higher (than expected, for example). Bestimmt is kind of similar, but emphasizes that the amount is known and fixed (and does not suggest it to be greater or less), while gewiss mostly suggests a greater amount. It depends on context whether gewiss suggests greater or smaller amounts, or neither.
From the samples:
Eine gewisse Summe means it wasn't free, but not necessarily a huge amount. It is often used to indicate that you have to pay more for better things:
Man bekommt zwar für 100 Euro ein Handy, aber eine gewisse Summe muss man schon anlegen, um etwas Anständiges zu bekommen.
Schon emphasizes that the amount is larger, but is not necessary here and may be colloquial. You'll often hear it in sentences like this though.
Eine gewisse Zeit means it wasn't instantly or fast:
Ich dachte, ich könnte auf GL&U schnell eine Antwort schreiben. Eine gewisse Zeit habe ich dann aber doch benötigt.
Eine gewisse Menge Lösung means you need some solution, maybe more than initially thought:
Ein paar Tropfen reichen nicht. Man muss eine gewisse Menge Lösung anwenden, um ein sichtbares Ergebnis zu erzielen.
The third example could also be changed to use bestimmt:
Man muss eine bestimmte Menge Lösung anwenden (nicht zu viel, nicht zu wenig), um ein sichtbares Ergebnis zu erzielen.
Gewiss can be inverted, for example by using nur:
Man braucht nur eine gewisse Menge Lösung anzuwenden.
This means that you need less than thought.
However, gewiss can not only refer to amounts, but also to other things and then has the original meaning of something known, but not mentioned (which is, of course, similar to the meaning explained above). For example:
Ein gewisser Kunde findet es sehr lustig, immer kurz vor Feierabend anzurufen.
The addressed person may or may not also know said customer in this case. This can be used to talk about the customer without saying the name.
Zu einer gewissen Zeit kann man auch mal schlafen gehen.
This suggests that you're staying awake for too long. The exact time is irrelevant.