Here's a link to Computers in Spaceflight: The NASA Experience. It has a lot of good material on those old computer systems. A cheap Palm Pilot has far more computer power than the Apollo Guidance Computer system, both in terms of memory and in computing power. In terms of physical size:

The Apollo Guidance Computer was fairly compact for a computer of its time. The CM housed the computer in a lower equipment bay, near the navigator's station. Block II measured 24 by 12.5 by 6 inches, weighed 70.1 pounds, and required 70 watts at 28 volts DC. The machine in the lunar module was identical.

Crew members could communicate with either computer using display and keyboard units (DSKY, pronounced "disky"). Two DSKYs were in the CM, one on the main control panel and one near the optical instruments at the navigator's station. In addition, a "mark" button was at the navigator's station to signal the computer when a star fix was being taken. A single DSKY was in the lunar module. The DSKYs were 8 by 8 by 7 inches and weighed 17.5 pounds. As well as the DSKYs, the computer directly hooked to the inertial measurement unit and, in the CM, to the optical units.

As for memory:

The story of memory in the Apollo computer is a story of increasing size as mission requirements developed. In designing or purchasing a computer system for a specific application, the requirements for memory are among the most difficult to estimate. NASA and its computer contractors have been consistently unable to make adequate judgments in this area. Apollo's computer had both permanent and erasable memory, which grew rapidly over initial projections.

Apollo's computer used erasable merry cells to store intermediate results of calculations, data such as the location of the spacecraft, or as registers for logic operations. In Apollo, they also contained the data and routines needed to ready the computer for use when it was first turned on. Fixed memory contained programs that did not need to be changed during the course of a mission. The cycle times of the computer's memories were equal for simplicity of operation49.

MIT's original design called for just 4K words of fixed memory and 256 words of erasable (at the time, two computers for redundancy were still under consideration). By June 1963, the figures had grown to 10K of fixed and 1K of erasable. The next jump was to 12K of fixed, with MIT still insisting that the memory requirement for an autonomous lunar mission could be kept under 16K! Fixed memory leapt to 24K and then finally to 36K words, and erasable memory had a final configuration of 2K words.

So, it sounds like the computers had 36K of 16 bit words (72 kilobytes) of fixed (Read-Only) memory and 2K of RAM. Hell, I think there are wristwatches with more than 2K of RAM!

I don't know precisely how fast the computer operated, but I did see a mention that the average instruction took 2 cycles (24 milliseconds) to execute. This suggests the computer was SLOW by modern standards.

The user interface was rather cryptic by modern standards, too, as described here.

The Apollo computer system made great demands on the crew. It took about 10,500 keystrokes to complete a lunar mission; not much in the life of an airline reservations clerk but still indicative of how computer centered the crew had to be. During the period in which the software was criticized for its complexity, designers attempted to reduce the number of keystrokes required to execute various programs. When possible, they also eliminated built-in halts as data were displayed for astronaut approval. However, the "fourth crew member" never abandoned center stage.

Apollo's crew employed its computer through the use of the DSKYs. In the CM one was on the main control panel opposite the commander's couch. The other was at the navigator's station in the lower equipment bay, where the computer itself was located. Block I had a different DSKY at the navigator's station than on the main panel, but they were identical in the Block II series. DSKY and computer activity could be monitored from the ground as the computer transmitted data words to drive real-time displays in Mission Control.

...

Astronauts used keys to enter information and select programs and actions. Key inputs caused automatic interrupts in the software. The astronauts would activate a program and then interact with it by requesting and entering information; a typical software load consisted of about 40 programs and 30 simultaneous routines. Changing programs and making other requests involved using the verb-noun system. Those familiar with current computer keyboards [58] will notice the lack of alphabet keys on the DSKY. Whereas most computer commands are entered by typing in the text of the command, the Apollo computer command list specified verb and noun pairs. There were 100 two-digit numbers available for each, and most were used on any given flight. Examples of verb-noun pairs are "display velocity" and "load angle." Verb 37, for example, was "Change Prog," which enabled the crew to set up a new program for execution.

If, for example, the crew wanted to execute the rendezvous targeting program, an astronaut would first press the VERB key followed by the digits 3 and 7, and then the ENTER key. That sequence informed the computer of a request for a program change. The astronaut would then press 3, 1, and ENTER to tell the computer to execute program P31. Within the program the crew could request maneuver angles (verb 50, noun 18), monitor the changes while a maneuver was in progress (verb 06, noun 18), or request the velocity change required for the next maneuver (verb 06, noun 84), among other functions. The CSM G&C Checklist, a set of "cue cards" on three rings changed for each mission by the Crew Procedures Division in Houston, described all these sequences in detail. The document contained reference data, such as a star list, verb list, noun list, alarm codes, error handling and recovery, and the checklists for each program carried in the computer.

Despite the 100 verb-noun pairs, 70-odd programs and routines, and a very limited user interface that alternated decimal and octal and blinked for attention, the consensus is that the Apollo computer was easy to use. As with other aspects of flying space missions, hours in simulators made operating the computer second nature. NASA engineer John R. Garman commented that "it's like playing the piano-- you don't have to see your fingers to know where they are". Familiarity with the computer, remarked astronaut Eugene Cernan, meant that pressing a wrong key simply and immediately "felt" wrong. Others also confirmed that using the machine eventually became relatively natural. Apollo astronauts were also willing to adapt to design foibles that would frustrate others. There were concerns that a crewman initiating a maneuver from the navigator's station would not be able to return to his couch before the burn started. In response, Virgil Grissom was accommodating: "Well, we'll just lie down on the floor". Astronauts also tolerated non-life-threatening software errors not cleared up before flight as merely something else to endure. They did, however, complain about the annoying number of keystrokes required during a rendezvous, so designers modified the software to make a "minkey" (minimum keystroke) option available, in which the computer could perform some functions without constant crew approval. This change contributed to an even more compact, straightforward system.

We've come a long way!