I'm starting to learn about antenna theory, feedlines, and different types of matching. I can build antennas etc from plans but I would like to be able to design my own and understand their characteristics. What software could I use to get started? Any tutorials? I'm interested mostly in high frequency and would like to venture into V/UHF, especially for amateur radio satellites.
One book I would recommend to you is the ARRL Antenna Book. With over 900 pages and containing both theoretical as practical construction examples this should give you a good start.
For antenna modeling software, one of the best programs is NEC, which is free and available on most computing platforms.
The Numerical Electromagnetics Code (NEC) is a popular antenna modeling software package for wire and surface antennas.
How it works
The code is based on the method of moments solution of the electric field integral equation for thin wires and the magnetic field integral equation for closed, conducting surfaces. The algorithm has no theoretical limit and can be applied to very large arrays or for detailed modeling of very small antenna systems. NEC models can include wires buried in a homogeneous ground, insulated wires and impedance loads.
Models are defined as elements of wire or similar as an input text file (typically in ASCII). They are then input into the NEC application to generate tabular results. The results can then be input into subsequent 'helper' applications for visual viewing and the generation of other graphical representations as smith charts, etc.
There is also EZNEC which is a windows program using the same computations but which incorporates a graphical user interface making it easier to directly plot data. Note that if you purchase the ARRL book it includes a special version of this program.