How do I figure out the right size seat post for my bicycle? I found a discarded Mongoose Alta frame with no seat post or seat that I want to refurbish.

How do I find out what size or type of seat post and seat I should get as suitable replacements?
The most important characteristic will be the seat post diameter. To determine it, measure the internal diameter of the seat tube, that is, the one which the seat post inserts into. Make sure you do not confuse it with the tube's external diameter, it is not needed.

Use a precision caliper for that, your measurements must be accurate to 0.1 mm. Do several measurements and then find their average.

Available bicycle seat posts diameters vary from 25.4 mm to 34.9 mm; maybe even wider or narrower posts exist. When looking for a new seat post, choose the one that has the diameter closest to your measurements.

The next characteristic would be the post's length. Generally, the length you want depends on your frame size (measured as letters XS, S, M, L, XL or numbers in cm/inches). Unless you buy a super-short one, however, there is less opportunity for a critical error with length. If nothing else, then a seat post that is too long can often be cut to be shorter. But if you make a mistake with diameter, it would be harder or impossible to accommodate that post to the frame.

The majority of saddles are compatible with the most of seat posts. Typically there are two metallic rails on the saddle and a clamping mechanism on the top of the seat post. In certain disciplines, like dirt jumping bikes, a saddle may be integrated to a seat post.