How to cost a researcher for a funding application?
Your institution/the institution that will host the project almost certainly has a grants office for the department/school faculty. You absolutely need to be in contact to do this costing as the institution almost certainly has policies and systems to deal with this that you MUST use if the institution is to sign off on your application. 

You don't say which country you are talking about, so let me answer for the UK. 

There are two ways to add the costs of a person to a grant application in the UK:

Types of cost

Directly Allocated Costs and Directly Incurred Costs.

DI costs are the easiest to explain. A DI cost is when the university has to spend money it would not otherwise have spent. So - buying equipment for the study, or travel costs etc. 

DA costs are where the university allocates a fraction of a resource it already pays for to the new project. So, for example, if a professor spends 10% of there time on the grant, then 10% of the prof's salary is "Allocated" to the grant. Universities like DA costs because they attract overheads, where as DI costs don't. Of course, this counts against you because it makes your grant more expensive to the funders. 

So, when you cost up a person on a grant, you need to decide DA or DI. Generally, if you are allocating a part of the time of someone already employed by the university, it will be a DA cost. If you are hiring someone new, then it is a DI cost (there are exceptions to this, but in general). 

For people that are already employed by the university, the university will have on its systems a "day rate" for that person. I.e. how much the university charges to have that person allocated to a project for a day. You then multiply this by the number of days a person will spend on the project. 

For new people, the university will often have a set number of salary points at which they can be appointed, with an associated pre-calculated cost. 

Our university has a costing tool that does all these calculations for you (and indeed, its use is mandatory, as it ensures that you have added all the correct extras, overheads, etc). 

Costing a fraction of a person

Funders generally want to know how much time a person will spend on a project. It is common to express this as either % FTE (Full Time equivalent) or hours. So one day a week would be 20% FTE, or about 340 hour a year.

If you are employing someone the university already employs, then this is easy. You say "The university will allocate 20% of Jane  Doe's time to the project."

If you are going the DI route, then this is harder, because they reviewer might well say 

"You want someone who has all these super advanced skills, but you will only employ them for 20% of there time for 18 months? Where on earth are you going to find someone who will agree to that?".

The alternative is you can name someone, even if they are not already employed. So you might say "We request salary and costs for 340 hours for a Dr. Chaudhuri to be employed as a research assistant, who will perform the vital roles of x, y and z".

My experience is that the more advanced the skills you want, the more skeptical reviewers will be of small FTEs, but that naming someone can go quite a long way to offsetting that. So 50% of an unnammed pre-doctoral technician is probably fine, but 20% of an unknown advanced software engineer is not, how ever 50% of the proven software engineer Dr. Alverez is probably okay.