Let's 1st understand what these planets represent on their own?

Venus - Venus is Beauty, Desire and Love, Liquid Money. Venus is the main significator of marriage. Venus represents girlfriend or wife for a man. Venus is the significator of all relations, may it be husband-wife or mother-daughter. Philosophically speaking, Venus is also the cause of all the sufferings in our life. How? Because Venus represents our desires and we get pain and suffering in our life only when our desires are not fulfilled.

Saturn - It is all that which we don't like in our life. Saturn is Delay, Frustration, Restriction, Limitation and Anxiety. It is people of Authority, like Boss at your Work Place or Father-Figure at Home. Saturn is our Karmic Debt from past-life. Saturn is the things we didn't treat too well in our past life. Saturn is our Challenges and Lessons of life. Saturn is Old-Age, Teeth/Bones in Human Body, Diseases, Changes etc. Saturn represents our Step-Relations, it means that wherever Saturn sits, people related with that house give us Step Treatment. Saturn is Hard Work, Efforts and most importantly Perseverance etc. Nothing comes easy and in one go with Saturn. You have to work hard continuously over the longest possible period of life. Saturn makes a person Legend as Legends have one thing in common that they choose one field and work hard in it for whole life. 

House Ruler - Besides these karaka things, Venus & Saturn will also rule some houses in your chart and will represent things related to that house. Of course we can't cover conjunctions Ascendant and house wise else it will never be over. So, you have to include those things at the time of interpreting this conjunction. Also, we need to keep in mind all Yogas and Raj-Yogas which their conjunction would be making to completely understand the conjunction. Here, we can only cover meaning as per karakas. 

Meaning of Venus-Saturn Conjunction - Although these two planets are mutual friends but Saturn is someone whom we can treat/consider as universal enemy as it is supposed to give hardship and challenges till mid-30s at least. So, no matter, where, with whom and in what dignity it is sitting in chart, it is supposed to give one or the other trouble. As Saturn represents delays and frustration, person will find meaningful love or relation only in his 30s. Early life relations can be full of trash. It is seriously recommended that this person must marry after 30 years of age at least. Likewise, other significations of Venus will take some time to develop like wealth, luxuries, arts, & creativity. Person may be required to work really hard at Venus related things with perseverance and those things will give results only in 30s. But good thing is that whatever we work on becomes our stronghold in life. So in later life, they are very creative and live a good convenient life in 30s. Likewise, their relations are much better in 30s as by that time they realize about how to deal with relations. It may even happen that by 30s, they become very cold or neutral about marriage or relationship or they have a very serious outlook for relations rather than romantic one. They have to work equally hard to gain there wealth. They can be working in field of finance, wealth and creativity. They can also be a relationship but they can be very serious or strict counsellor. 

Who will win the Conjunction? - Saturn will, at any day. 

Dignity & Strength - 

No matter where the conjunction is, Saturn will have a hold over Venus, but still this conjunction can work best in Libra where Venus is in own sign and Saturn is exalted. 

It can also do well in Taurus, Gemini, Capricorn and Aquarius where both remain in good dignity. 

Pisces is also a good sign as Venus is exalted and Saturn is in neutral dignity. 

In Sagittarius, both are neutral. 

Real problem comes when they are in Aries where Saturn is debilitated, in Virgo where Venus is debilitated and Cancer & Leo where both are in enemy signs.