Over at White to Harvest there are some very stimulating discussions of election and assurance going on - see here and the comments here. But just to stick up for the reformed tradition, here are (very selective!) quotations from three of the greats. Not to say that these are consistently followed by each theologian or their tradition but here are some good bits nonetheless:
Faith: "is a firm and sure knowledge, of the divine favor toward us, founded on the truth of a free promise in Christ, and revealed to our minds, and sealed on our hearts, by the Holy Spirit" (Institutes, 3.21.2.)
"Christ, when he illumines us into faith by the power of his Spirit, at the same time so engrafts us into his body that we become partakers of every good." (Institutes, III.2.35)
"Many persons want to know their election before they look to Christ, but they cannot learn it thus, it is only to be discovered by ‘looking unto Jesus.' If you desire to ascertain your own election; after the following manner shall you assure your heart before God. Do you feel yourself to be a lost, guilty sinner? Go straightway to the cross of Christ and tell Jesus so, and tell Him that you have read in the Bible, ‘Him that cometh unto me, I will in no wise cast out.' Tell Him that He has said, ‘This is a faithful saying, and worthy of all acceptation, that Christ Jesus came into the world to save sinners.' Look to Jesus and believe on Him, and you shall make proof of your election directly, for so surely as thou believest, thou art elect. If you will give yourself wholly up to Christ and trust Him, then you are one of God's chosen ones; but if you stop and say, ‘I want to know first whether I am elect', you ask what you do not know. Go to Jesus, be you never so guilty, just as you are. Leave all curious inquiry about election alone. Go straight to Christ and hide in His wounds, and you shall know your election. The assurance of the Holy Spirit shall be given to you, so that you shall be able to say, ‘I know whom I have believed, and I am persuaded that He is able to keep that which I have committed to Him.' Christ was at the everlasting council: He can tell you whether you were chosen or not; but you cannot find it out any other way. Go and put your trust in Him and His answer will be - ‘I have loved thee with an everlasting love, therefore with loving-kindness have I drawn thee.' There will be no doubt about His having chosen you, when you have chosen Him." (‘Knowing, brethren beloved, your election of God.' Morning and Evening, July 17. 1 Thess 1:4.)
"If we would know who God is, and what is the meaning and purpose of His election, and in what respect he is the electing God, then we must look away from all others, and excluding all side-glances or secondary thoughts, we must look only upon and to the name of Jesus Christ, and the existence and history of the people of God enclosed in Him" (Church Dogmatics, II/2, p54).
"We must not ask concerning any other but Him. In no depth of the Godhead shall we encounter any other but Him... There is no such thing as a decretum absolutum. There is no such thing as a will of God apart from the will of Jesus Christ... Jesus Christ reveals to us our election as an election which is made by Him, by His will which is also the will of God. He tells us that He Himself is the One who elects us... As we believe in Him and hear His Word and hold fast by His decision, we can know with a certainty which nothing can ever shake that we are the elect of God" (II/2, p115).
Here is my favourite from Barth:
"We might imagine the conversation to which it gives rise and some of the forms which it necessarily takes. The man to whom it is said thinks and says that he is not this new, peaceful, joyful man living in fellowship. He asks leave honestly to admit that he does not know this man, or at least himself as this man.
The Word of grace replies: 'All honour to your honesty, but my truth transcends it. Allow yourself, therefore, to be told in all truth and on the most solid grounds what you do not know, namely, that you are this man in spite of what you think.'
Man: ' You think that I can and should become this man in the course of time? But I do not have sufficient confidence in myself to believe this. Knowing myself, I shall never become this man.'
The Word of grace: 'You do well not to have confidence in yourself. But the point is not that you can and should become this man. What I am telling you is that, as I know you, you already are.'
Man: 'I understand that you mean this eschatologically. You are referring to the man I perhaps will be one day in some not very clearly known transfiguration in a distant eternity. If only I had attained to this! And if only I could be certain that even then I should be this new man!'
The Word of grace: 'You need to understand both yourself and me better than you do. I am not inviting you to speculate about your being in eternity, but to receive and ponder the news that here and now you begin to be the new man, and are already that which you will be eternally.'
Man: 'How can I accept this news? On what guarantee can I make bold to take is seriously?'
The Word of grace: 'I, Jesus Christ, am the One who speaks to you. You are what you are in Me, as I will to be in you. Hold fast to Me. I am your guarantee. My boldness is yours. With this boldness dare to be what you are?'
Man: 'I certainly hear the message, but...'
In this perplexed and startled 'but' we see the attack, and who it is that is attacked." (V/2, p250)