Ask the building department that issued the permit, the only place plans are ever filed: in the valley that is Clark County or the city of Las Vegas, Henderson or North Las Vegas, and because retained residential plans are commonly limited, the builder, the original architect and the assessor's sketch are the usual fallbacks.
Two things get called blueprints and they are not the same request. One is the permitted construction drawings for your specific house, which exist only if a department kept them. The other is a dimensioned floor plan good enough to plan a remodel, sell a house or figure out where a wall can move, and that one can be produced whether or not the original drawings survive.
Decide which you need before you start, because the first can be a dead end and the second never is.
Start with the building department
Permits are pulled from the jurisdiction the house sits in, so the first step is establishing which one that is: an address with a Las Vegas mailing address may be in unincorporated Clark County rather than in the city. The assessor's parcel record names the jurisdiction, and most departments have an online permit search by address or parcel number that will show what was issued and when.
Then ask for the plans on file for that permit. Retention practice varies widely and is the reason this so often fails: commercial plans are commonly kept, single-family residential plans commonly are not kept indefinitely, and homes built before permitting was computerized may have a permit record with no drawings behind it. Expect a written records request, a copying fee, and a wait measured in days or weeks rather than minutes. Nevada's public records law is NRS 239 and the department's own retention schedule and fees are worth confirming with them directly.
Why they may need the owner's authorization
Architectural drawings are commonly copyrighted by the architect or designer who made them, so a department that holds a set may release it only to the owner of record, or only with the designer's written consent, and may allow viewing rather than copying. This is general information rather than legal advice; the department will state its own rule, and where a dispute arises a Nevada attorney is the person to ask.
Practically this means going in as the owner, with proof, rather than as a curious buyer. A buyer under contract can usually get the seller to make the request or sign the authorization, and that is the moment to do it, because it is far harder afterwards.
The other places a set of plans lives
The builder, first, on a production home. Large builders keep master plans by model and community, and a home built in a valley subdivision in the last few decades is one of a few hundred identical floor plans. Give them the community, the model name off the original sales paperwork and the year, and a plan sheet is often available even when the county's file is not.
The original architect or designer keeps their own archive on a custom home, and is the copyright holder anyway. Previous owners frequently hand a set over at closing and it ends up in a garage or an attic. An HOA architectural committee may have the plans submitted for an addition or a pool. The pool, solar or addition permits filed since construction commonly have their own drawings, and those are often better kept than the original house plans.
When you cannot find any, which is common
The county assessor's record is the free fallback and it carries more than people expect: square footage, room and bathroom counts, the year built, the lot dimensions and usually a simple sketch of the building footprint. That is enough for many questions, and it costs nothing.
For anything more, hire the drawing rather than hunt for it. A designer, architect or drafter will measure the house and produce as-built drawings, and a permit for a remodel will require new stamped plans regardless of whether the originals turn up, so a remodel budget is already paying for drawings. A laser measure and an afternoon produce a workable dimensioned floor plan for free. What none of these give you is what is inside the walls, and that is what a house's original plans were mainly useful for: for structure, load-bearing walls and slab plumbing, the answer comes from an engineer, a scan or an exploratory opening, not from the archive.
Questions people ask
Are house plans public record?
The permit record generally is, and the drawings behind it often are not fully open: copyright in the architectural work and the department's own rules commonly limit release to the owner of record or to someone with the designer's consent.
How much does it cost to get plans from the county?
Where a set exists, commonly a per-page or per-sheet copying fee plus a research charge, so tens of dollars rather than hundreds. New as-built drawings from a designer cost far more, and the quote depends on the size of the house.
How do I find out if a wall is load-bearing without the plans?
A structural engineer inspecting the attic, the framing direction and the foundation will say so, commonly for a few hundred dollars, and their letter is what a building department will want anyway before permitting the removal.