Great that you should ask - this is something I have been looking into myself.
I have been taught that as Christians we are here to win souls for Christ - otherwise we would be taken straight to heaven once we got saved.
So - my two cents on effective ways to spread the gospel?
There are a number of ways that I am aware of.One would be friendship evangelism - where one actively cultivates relationships with the intent of loving others into the kingdom.It can be a costly and self sacrificing activity and difficult - especially as in my experience - not everyone will be interested in knowing Jesus and may seek to take advantage of your kindness - but (so I am told )- it is one of the most effective ways of bringing Christ to the lost.
Then of course there are gospel tracts, which can be distributed in public places such as train stations or just on the street.If this is too confrontational for you, you can also consider leaving them anonymously in phone booths, library books, rest rooms,or on benches in shopping malls.Jack Chick has a myriad of tracts which come in the form of cartoons - making them more likely to be read.
Chick Cartoon Tracts
Remember that although it's great to evangelise in your neighborhood - there are millions who have never heard the name of Jesus - who live in what we call the 10/40 window.
Joshua Project - The 10/40 Window
I strongly believe that evangelism is not just a matter of telling the gospel , but should be accompanied with prayer.One way of reaching the unreached who do not have access to the bible or to missionaries/churches is to pray for them.Operation world is a fantastic organisation which documents christian activity all around the globe and raises issues for prayer.
Operation World | Home
Finally, we need to remember that when we seek to live lives which are characterised by integrity, repentance and the power that comes from reading the Word and speaking to Jesus regularly - people will be naturally drawn to us, because they will see the light in our lives.We can then bring them to church, where they will recieve input from other christians and be able to see how a loving community of Jesus-Followers deal with the issues of life.After all,teamwork has its own sort of synergy and the christian life was intended to be a communal endeavour.
One word of warning - when you evangelise others, you are on the offensive - so expect opposition from the enemy - he likes to stir up trouble for those christians who seek to plunder his kingdom.So be prepared - bathe your efforts in prayer and know your stuff - ie. the bible - be clothed in the armour of God (Ephesians 6:10-18)
Also, don't be disheartened if you do not have immediate success - we are just called to be faithful and sow seeds - it is God that gives the increase.(1 Corinthians 3:6)Sometimes people remember seeds which have been planted a long time ago and only then decide to make a decision for Christ - so every bit counts.
Hope that helps.