I've been doing a lot of standings grinding lately to lower broker fees.
For faction standings like Caldari State I've been doing Data Center missions (mostly pirate tag turn-ins) which give some fairly substantial standings increases.
For corporation standings (Caldari Navy for example) the usual way is to do missions for the corporation in question. However, unlike with faction standings, corporation standings can be shared with anyone in the same fleet. You don't have to help them do the mission. You don't even have to be in the same system or region. You can be sitting in a station while AFK, all you have to do is be in fleet with them, which means you can hire someone else to the grinding for you.
I did some searching and quickly found a service that specializes in grinding corporation standings. TSCA (The Standing Correction Agency) has a very good reputation so I decided to give them a try.
The Standing Correction Agency is a business which provides personal standing increases via fleet mechanics for clients. Their normal service is for standings up to 8.0 with corporations only, for example with Caldari Navy, Home Guard, or Ministry of War, but not faction standings like Caldari State or Amarr Empire.
Beyond that, if you want faction standings or corporation standings beyond 8.0 you can always try talking to them about it. They might agree to do it but only on an individually negotiated basis.
After having TSCA grind standings for me on 2 different characters, Republic Security Services 1.5 to 3.0 on one character and Caldari Navy 1.52 to 8.0 on another, I'm very pleased with the service. Everyone involved was courteous, professional and efficient, right from the initial contact with Imiarr Timshae all the way through to the end with the two pilots who did the actual grinding.
I was particularly happy with the Caldari Navy grind. I expected it to take at least a week and probably longer but it only took 3 days. It did help that they had two pilots with 2 characters each working on it for me. Many thanks to Tovar and Drake for getting that done so quickly and for being so friendly during the entire process.
I will almost certainly be using TSCA again in the future and very highly recommend them to anyone else looking for help grinding standings!
BTW, are machs FoTM now? I've been seeing them all over the place lately.