It depends on your budget and where are you traveling from..
Its a long journey so choose your option accordingly
-You can travel in Local transport buses (HRTC) from manali/shimla to kaza.
- Hire a taxi from delhi/chandigarh/shimla
It depends how are you going and when?
via manali remains close at kunzum pass in winters, you can go via recongpeo.
there are hrtc buse till kaza, in break journey
delhi to Shimla, shimla to peo, peo to kaza, but you have to check at the base depots if the bus is in service(because of covid-19). that's for local transport, othewise, bike or car is always an option
There are two routes to spiti, one from manali and the other from kinnaur. there are buses or the routes or you could get a cab/rented vehicle. There are also shared cabs that go from manali to spiti which you can pre book from manali.