This is just an add-on to @rrg's answer. The first thing I recommend that you do is to talk to your manager and get a better grasp of the project scope (which you may have done already). More specifically, are they asking you to build issuer level curves (doesn't sound that way), or sector curves (more likely). How do they plan to define the sectors (by rating? by industry? etc.) This can easily become a very large project, so it's important that you know exactly how far they want you to progress.
Now back to tackling the project. @rrg already mentioned that there are really just two steps. With regard to security selection, the rule of thumb is straightforward: 1) If at all possible, pick or overweigh bonds that are liquid, with good pricing information; 2) Select bonds that are comparable and representative of the market of interest. This is not a science and lots of art is involved. For example, this answer provides some tips (NOT rules) on what bonds can be included in building the US Treasury curve – there are a lot of nuances. For corporates, you should at least make sure that the issuers are of similar credit quality and go from there.
You then proceed to fit the curve. For corporates, parametric models (e.g., Nelson-Siegel, Svensson, even single piece "splines") are very popular, particularly if you don't have a lot of bonds that span the entire maturity spectrum. Don't reinvent the wheel. Look at existing codebase (e.g., Quantlib) and go from there.
Finally, some references: