Per's advice on recording a tape to WAV is the simplest way to get started, but may not yield perfect results. There are some special cables you can build or buy, called
X1531 or possibly a regular XE1541 cable if you use the C64 as a slave device when transferring from tape to PC. However, unless you made a lot of own programs, chances are that 99% of your games already are archived somewhere on the Internet, in one form or another.
As for loading, since the C64 uses a proprietary tape recorder you can't quite connect a MP3 player to the input. There exists some MP3 cassette inserts it has been speculated whether they could be used. Another way is to build or obtain a third party tape recorder device which lets you connect a regular tape recorder or other sound source.
However, you mentioned memory cards and in that way you're lucky. For the C64 today there are many different solutions:
*
uIEC by Jim Brain. It is available with both SD and CF interfaces
* MMC2IEC, SD2IEC, 1541-III (see above Wiki link for further linkage)
*
1541 Ultimate, like the above but focused on 100% perfect floppy drive emulation
*
MMC Replay, a combined freezer cartridge and MMC interface
There exists a few more projects, like the
DC2N which is a digital cassette player that apparently both can be used to take backups of old tapes to a SD card and also play back those files on a real C64.
Basically, if you dig around and frequent Commodore forums, you will probably hear and read about even more projects. Many are experimental one-offs, while a few go to commercial production. Many projects overlap eachother so it may be a bit of a jungle which one(s) you'd like to get.