Schengen visa overstay

Unfortunately, there is not much you can do to overcome this easily. Among the possibilities:

• Waiting. You did not get a lifetime ban or anything, this minor infringement is just one of the factors going into the decision. As time passes and especially if you are able to document a stable situation in your country of residence (buying a house, founding a family…), you will be more likely to get a visa.
• Travel to other countries. A history of travel to other countries will look reassuring to consular officers. If you are someone who travels a lot and had many occasion to (over)stay in a (rich) country but did not do it, you will appear less likely to abuse a visa. On the other hand, a recent overstay in the Schengen area might very well adversely impact other visa applications, including to the UK.
• Move to Europe. If you have a good reason to move to a Schengen country (family, sponsored job…) and manage to get a residence permit (not easy, obviously!), the short-stay rules become essentially irrelevant. You will be able to leave and enter the area without worrying about your earlier violation of the rules.
• Change citizenship. Not really a practical strategy or something you should consider just to overcome this but acquiring the nationality of a country whose citizens do not need a visa would make it much easier to enter.