First, I'm gonna assume you want to replace your iron railing system with, say, an oak one. IF this is the case, read on. If not, forgive me for not answering your question ...
About 5 years ago, we too had a wrought iron railing going up the stairs from the 1st floor to the 2nd. We've since replaced it with oak.
I didn't do this job myself. I enlisted the help of a friend who 'knows what he's doing' and I acted as his helper. I was impressed with all the 'little' things that one needed to know to do this job. Granted, it was a straight run up the stairs but that's where the easy part ended.
Our original iron railing was set on a knee wall; not on the treads. Hence, we removed the one-piece railing and then installed an oak knee wall. On top of that, we installed a shoe rail. And in the shoe rail, we installed our balusters and fillet. As we worked our way to the top, when the 'opening' between the top rail and the shoe got smaller, we cut from the TOP end of the baluster. In doing this, you get the 'illusion' that the rail went all the way to the 2nd floor. (Ours 'terminated' at the ceiling about 2/3rds of the way up.) Depending on your stair set up, your iron railing system may be installed on the treads, and go all the way to the top of the stairs. As I said, ours was installed on a knee wall and we could only go 2/3rds of the way up. IF you have my thpe of 'system', you really can't install a new system on the stairs because you MAY not have enought 'width' on the tread to do so. IF you have very wide treads, you may be able to do this.
As Henry says, it's not so easy to do. Getting the right angle, for starters, is key. Anchoring the newel post is key too. You must keep a vertical 'line' too. In short, if you mess up anywheres along the way, you will have made a very expensive mistake. IF you want to save some $$$, talk to a contractor for a materials list. Buy a few extra balusters too for 'mistakes' or future replacements. Keep any scraps that might be usable, such as extra fillet. Then, if you're staining the system, do it yourself. Only apply 1 coat of poly (for protection) until the contractor is finished. I found that the finished job looks much better when the staining is applied BEFORE the stair is installed. The contractor will have to cut the fillets and railing and post and so on IN ADVANCE of the installation. Oh, and be sure to sand everything BEFORE you stain! We got our oak from Home Depot. We saved more than HALF the cost of the material by getting it there. (A local lumber yard or 2 had the SAME oak 'system' for much, more $$$.)