The first thing I would like you to do is make sure your fitting chute is tied down. I know first hand the wreck you can have if it is not and you steer freaks out and takes off with it; your steer can become injured, and at the very least all the hard work you have done will be lost.
Now the fun part; you need to get your steer in the chute; if you have done all the ground work listed above it won't be to hard. If your steer is still a little hard to lead take your time, and add a safety rope tied to something I tie mine safety rope to the post that right next to the chute. Next take the lead rope and run it through the chute and hopefully they walk right in. If your steer does not walk in use the safety rope to get them back up to the chute and start again. Just keep working and talking to them and they will go in.
Once you have them in the chute for the first time you will want to tie their head up and just comb them; I do this with each of my steers; I want my steers to like the chute.
each one of my steers had their moment in the chute I like them to be in the chute for at least 30 minutes the first time.
In a day or two I will but my steers back in the chute and use the blower and turn on a pair of clipper and before you know it your steers are loving the time in the chute.
This is what works for me; when working with cattle sometimes you just play it by ear and go with what works.