The advantage of all offmeta picks
When playing an offmeta champion your enemy will most likely not know how to play against you, for singed this is amplified due to the fact that singed is a top-laner so most botlaners have never laned against a singed. Then you can add the fact that they will have also probably never seen a singed at all due to it being considered off-meta even for the toplane. You can use this to your advantage by playing mindgames against your enemy, giving you yet another tool to use.
The beauty of singed
If you get fed up with your carry you can just ignore them and take matters into your own hands. Just start building as you would any other singed game, and go roam a little, contest objectives, gank some lanes and then whenever you feel like it you can proxy to catchup yourself. Otherwise if you're feeling especially pissed you can just sell your sup item and proxy sidelane like a real chad.

Basics:
The most important part of singed sup is knowing your limits. The reason why it "works" is because not only does the enemy not expect you to survive, they also don't expect you to win. Singed support is all about surprising your enemy with your survivability and your damage. Usually, as long as you dodge one or two skill shots you should win the fight. How you should play the lane is by sitting in the edge of a bush and as soon as an enemy walks us enough for you to be able to hit them with the inner edge of your max range glue then you will be able to ground them and catch up to them without them being able to get away. As soon as you fling them towards your carry you should either fake that you're going towards the other enemy or commit towards the other enemy until you tag them with the poison. The objective of doing so is so that you can make sure that the one tanking and the one they are paying attention to is you since you can *almost always survive and kill the enemy or survive and get away safely as long as you have got your summs. The moment you either start tanking the other player, be it the support or the adc you want to go back and fight the initial player, by then your poison should be about to run out and your fling and passive should be almost up. Your carry will have almost always left the enemy very low so you should think to either commit to the kill or finish up the trade. Most lanes will be played along those lines, you should just make sure the matchup allows for you to win when playing like so. For example against champions like Soraka, if you manage to dodge her slow and fling her it is a guaranteed win or you will at least burn heal and or flash; Same with Lux, if you dodge her Q and fling her then the win is pretty much secured, for that reason against these types of champions a flash is recommended so that you can flash over the skillshot allowing you to catch them off guard leaving them unable react. Against tank supports like Nautilus or Blitz you should try to focus on the adc instead, the only situation in which you may have a chance in winning is if the enemy misses either one or 2 skillshots and you are able to proc your after shock faster than they can and even then it's up to your carry to win the fight as all you are doing is giving them an advantage. Another thing to keep in mind is the adc themselves; high damage adcs(like Kai'sa or Jhin), carries that can either stick to you very easily(like Ashe) or kite you just as easily(like Lucian or ezreal), are all factors to keep in mind Especially when combined with a support that counters you. As long as you are aware of what you should dodge or wait for the cooldown to be down for then you should be fine.

Ahead with useful carry
Once laning phase is over your playstyle can differ a lot as you now have many options at your disposal, what you choose should be decided based what you think will lead your team to victory. If you are ahead you will most likely always go after the enemy botlane along with your carry with the intent of extending your lead even more and most importantly getting them fed enough to the point where you wont need to babysit them anymore. Once that's done you can focus on helping someone else get fed or prevent the enemy from getting even stronger off a weak teammate, that's mostly how you would go about playing to have the highest chance at winning.
Playing from Behind
In this case you should assess the current state of the game and make a calculated decision on how you could get someone fed to carry you. Most likely that would mean to look at your team and see who is the strongest player and start camping their lane, singed excels at 2v1 situations especially if you are have at least one item. A good build path for these games is the Shurelya's build path since it provides the most playmaking opportunity necessary for these types of situations.

How did you get here?
If you somehow manage to get to late game you should start considering pushing sidelanes by yourself, by now you should have enough ap to almost melt waves, you can also easily relieve pressure from a lane by quickly proxying half the wave and leaving quickly. Taking advantage of this is crucial to winning a game on singed support. You can also consider taking the Elixir early due to the ap and most importantly the damage you get on towers. This combined with your demolish makes you a threat they are unable to ignore. Once you finish your whole build you can start replacing the support ward and mythic items depending on what you need in the game. Most likely what you will need is damage and speed, the best mythic replacement has to be Lianry's due to its almost instakill potential on squishies.