Remove all previously used equalization and effects, or start from a raw copy of the original vocal track. Evaluate the sound of your voice by itself without instruments. Take note of strengths and weaknesses, things such as nasal tones, sibilance (harsh "ess" sounds) and fullness.
Apply EQ to the voice to counter the flaws and highlights you identify using the EQ provided with your DAW or a suitable plug-in. As a general rule, remove frequencies first, add only if necessary; and, at this stage, make small adjustments, between 2 and 5 decibels.
Use pitch-correction software if it is available and required to correct the performance. Additional processing may make it more difficult to correct pitch, so generally it is applied at the earliest stages of post-processing.
Use a compressor to even out volume levels and give your vocal a professional edge. Most DAWs have compressors, limiters and other dynamics processors included. Choose one that allows control of threshold, ratio, attack and release. Threshold setting will depend on the level of the recorded track. Start with a ratio between 2-to-1 and 5-to-1. Experiment with attack (how fast the compressor works) and release (how fast it stops working) to fit with your song. Try extreme settings and work backwards until you are comfortable with the compressor's effect.
Use an automatic double track effect to thicken your vocal sound. Time-based effects such as delay and chorus, used with moderation, can give the effect of two voices with one recorded track. Many delay plug-ins will have ADT presets.
Add reverb to the vocal if a sense of space is desired, but be aware that too much will cause the voice to blend in with instruments to the point where it becomes indistinct. Your ear will get accustomed and desensitized to reverb after time, so check your remix frequently with headphones or secondary monitors.