The fastest at usually the least expensive way to change your amps tone is changing out preamp tubes. Primarily in Preamp Valve 1 (which is generally the preamp tube farthest away for the power tubes) and Preamp Valve 2. If the amp is two channel, V1 shapes the tone of channel 1 and V2 for channel 2. Try a few different new and New Old Stock brands out and let your ears be the guide.
 
 A more subtle way to change your amps tone an is still fairly inexpensive ( unless your buying a boutique cable!!) is to try different guitar cables. Some cables let more signal through to the amp ( the lower capacitance cables) This may be good or may not depending on how you set your amp and the tone your looking for. Stevie Ray Vaughn did not like hot guitar cables, primarily because his amp setup was giving him enough drive already. Stevie's long time amp tech Cesar Diaz affirms to this saying that Stevie insisted he go down to Radio Shack and get him a coil cable after Cesar had given him a monster cable to try out. SRV just thought the Monster cables were too hot.
Try some different guitar cables out and listen to the differences. Keep your guitar and amp settings the same to help hear the differences.

 Here is one of my favorite ways to change the amps sound. Ok you do need to know how to use a screwdriver, read polarities and possibly solder. You guessed it! Change the speaker out. This is the final transducer to your ears. If the amp sounds amazing and your speaker is junk then your tone will be junk also. There are many different varieties of speakers on the market and 10 musicians will tell you that the think brand x and model y is the best. It all has to do with what sound your looking for. What you already have, Guitar, amp, effects, etc. You want a speaker that can handle the amps wattage. So at least shoot for a 25% mark up when changing a speaker out. If the amp is 50 watts then use a 75 watt speaker. 
 
 Be careful most Boutique amps today or under rated when it comes to wattage. Primarily because of the over designed output transformers they are using. You can put a 40 watt Fender Super Reverb up to a Carr Slant 6V which is rated 40 watts and the Carr is much louder. Dr Z's Maz Jr is rated at 18 watts hoever it is putting out 24 watts at full volume!

 There are different magnets, voice coils, cone material, dB sensitvities, basket designs etc to take into account when purchasing a speaker. It can get expensive and time consuming trying out a bunch of different speakers. Ok the time consuming part is not much of a burden unless the speaker sounds really bad.

 AlNiCo vs Ceramic. I get alot of phone calls about this topic. The Vintage purists will usually go with AlNiCo and the more modern players usually go with the Ceramic. Not always the case but more than likely. Some musicans combine the AlNiCo and Ceramic speakers into 1 enclosure or different enclosures. You can then get a blend of the two different sounds. They definately have their own unique characteristics. In my opinion the AlNiCo has a looser low end response than the ceramic speaker however the mid- high range in the AlNiCo is sweeter and the high end sounds more rolled off which yields a slightly smoother high end response. We won't even get into Neodymium magnets at this time but feel that the learning curve is starting to come around as OEM's are starting to produce some really good sounding Neo speakers. And if I can 1 day get my 64 Super Reverb weighing less than 55 pounds and the tone sound just as good you bet that is enticing!

 Hemp cone vs Paper cone Some people love it some people dislike it. Hemp is definately stronger than paper cones which means they should stand the test of time. I heard stories about a guy who bought 40 year old NOS cones and having them installed in the speaker baskets only to have them blow to bits. The paper becomes brittle with age and the paper will break down from time and environmental factors. That is why I always advise any Vintage speaker owner to shelf the original speaker and put in a substantial replacement in case they  want to sell it with the original speakers still functioning.  Hemp is stronger simply because hemp fibers are longer than paper fibers and when they are bonded together they create a stronger bond.

 Sound wise I think the hemp sounds smooth and has alot of midrange to offer. Midrange is good we all know but having a set up with too much midrange can cause ear fatigue. If you have a Marshall which already has a more pronounced midrange tone stack it may be overkill in my opinion. I like the hempcones with a Blackface amp which has a mid scooped tone stack.

Ok i hope I haven't bored you to the point of hitting the x button because this can really help out your sound if you want your amp to have more or less loudness. Choosing a speaker with a higher dB sensitivity rating such as 100 can get the efficiency up in an amp that needs more volume. And vise versa, Putting a speaker rated at 90 dB sensitivity can quiet down a  loud amp. A + or - 10 dB difference is twice or half as loud. The speaker is the final transducer, Don't let it be the weakest link in your signal chain.