Well pump work spans a wide range of difficulty depending on which type you have — it's worth being honest about which end of that range you're on before you start.
A shallow jet pump — mounted above ground, all fittings and wiring within arm's reach — is a job a genuinely handy homeowner can take on: comfortable with basic electrical (disconnecting and reconnecting a 120V/240V circuit safely), comfortable with plumbing unions and PVC or galvanized fittings, and willing to read the manufacturer's install instructions closely. It's still work with real failure modes (a bad union leaks, a miswired motor won't start or trips a breaker), so budget the time to do it carefully, and confirm your local code doesn't require a permit or licensed installer even for above-ground work — some jurisdictions do.
Replacing a submersible pump means pulling every foot of drop pipe and submersible wire out of a well casing — often 100, 200, 300+ feet of it — then lowering a new assembly back down without damaging the wire's splice or dropping anything down the casing (which can mean re-drilling the well; a real and expensive failure mode). Contractors do this with a truck-mounted well-pulling rig or a pipe-pulling tripod rated for the load; without that equipment it's not just harder, it's not safely doable for most homeowners. This is the job to hire out, full stop, for any well deeper than a jet pump can reach.
Many states and counties require well modifications — sometimes including pump replacement, sometimes just well construction changes — to be performed or permitted by a licensed well contractor. Requirements vary a lot by state; check with your county health department or state water-resources agency before starting any well work, DIY or otherwise. This isn't optional paperwork in some states — unpermitted well work can complicate a future home sale.
Well pump circuits are typically 240V, run near water, and often on a dedicated breaker with a pressure switch in the loop. If you're not confident isolating and testing a circuit safely, this alone is a good reason to bring in a licensed electrician or well contractor rather than working live.