For Singapore you either need to have a local contact to provide a Letter of Introduction and do the online side for you to apply directly for a visa, or you need to go through an authorised agent.
Any visa agent may offer to do it, but since all they will do is engage an authorised agent then you are paying for someone else to do something that you might be able to do alone.
The Singapore ICA has a list of authorised agents in India by region, and the list can be found on the Singapore Consulate in India's pages as well last time I looked.
For Singapore visa, you have to go through an authorised visa agent as listed on the Singapore High Commission website:
If you know someone in Singapore, they may help you apply for a visa on the ICA website.
For Malaysian visa, you can do it online at https://www.windowmalaysia.my/evisa/evisa.jsp
Apply through agent. Select a tour package and the tour agency usually will help.
Indian passport holders can not apply for singapore visa on their own. The application goes through authorized visa agents only. The list of the authorized agents is on the high commission site.
Contact one of the listed authorised visa agents for Singapore visa.
You can search the Malaysia forum for more details regarding this.
Depending on your itinerary, if you enter any of these countries twice, you will need a multiple-entry visa instead of a single-entry visa.
Singapore High Commission has a list of Authorized Visa Agents for each region in India. They charge a minimal service fee of INR 300 over and above the Visa fee of SGD 30. You can drop off the documents and passports to them and they take the burden off of you. Withing 3-4 business days, your passports are ready to be picked up with your visa stamps.
For Malaysia visa, if you are a resident of India and going to Malaysia for less than 15 days either direct or via Singapore, Thailand or Brunei and returning direct or via Singapore, Thailand or Brunei, then you are eligible for an eNTRI visa. You can apply online at https:/…evisa.jsp. Withing a day of uploading all documents on the site, the eNTRI note is sent to your email to be printed and taken along while entering Malaysia.