Salvation is all about Christ's work on the cross and not what we do. All we have to do is believe in Jesus( that he is God incarnate, died for our sins, rose again by the power of God), confess with the mouth " the Lord Jesus or Jesus is Lord" ( see Romans 10:9) and ask Jesus to save us. Romans 10:13 says: " everyone who calls on the name of the Lord will be saved."
It also says that those who trust in the LORD will not be condemned. ( see Psalm 34:22). Therefore, those who trust in the Lord Jesus for salvation, will not be condemned. This is how one can know they are saved biblically. How one can know they are saved personally is a different matter all together.
I often have struggled in the past with knowing I was saved. I high school I was constantly asking Jesus to save me. For a while I could not call God Father. Then after having a mature Christian pray for me to be filled with the Spirit, I was able to call God Father. For some, getting filled with the Spirit helps a lot with assurance of salvation. For me even after that, I had uncertainty. At some point OCD got really bad and I started asking God to save me even more than I did in high school. The last time I asked Jesus to save me, I also was saying I am trusting in you to save me and may have also said something to trusting in your blood to save. I would say that I was trusting in him to save me, rather than just keep on asking him to save me because maybe I did not say it right or just want to be sure. Asking Jesus to save you constantly though, does not help to assure one that one is saved. Right now I am resting and trusting in Jesus to save me. I have not been asking Jesus to save me again, I am trusting that he already has. His blood shed for me and my faith in him is my plea.
It is possible to be assured that one is saved and yet have doubt in the back of the mind that says " what if I will be condemned because I didn't forgive and thought I did, or I coveted too much or sinned too much, or was too fearful of things... ?Etc. In order to attack the doubt, you got to go to the source. Why is it that you have some doubts? Do you feel you have to do enough good works for God to accept you? Do you think you are sinning too much and might be condemned for it? Do you have struggles with OCD? And what are you trusting in?
Even after attacking the source of the issue, one may still have some doubt. That is ok. That is where faith and Scripture kicks in. Certainty without doubt does not need to be the goal. Complete certainty without doubt of the validity of the essentials of Christian faith is not required of someone in order to be a Christian. Neither does a person need to have assurance of salvation without doubt in order to be saved.