It strongly depends what you want to top up with and I assume that the goal is top up monzo from other currency.
If you are the owner of other debit card or bank account - you select ‘myself’. It means you are sending money from you to you.
If you are not the owner of card/bank account, but it’s account that belongs to family memeber (example), and you would like to receive money from them - your family memeber should select ‘someone else’. It will be transfer from family member to you.
If you are sending money between you and someone else, both people need to have an account. Accounts require ID verification (passport ideally), which is most likely done for the anti-laundering legislation.
Once accounts are ready, it’s fairly straightforward.
Person who sends the money (you or family member) has to initiate the transfer, and choose option - card or bank transfer. Then as you go along, you will define details of the recipient, that being you.
How to define that money needs to go to Monzo? You need to use details from this post:
Please make sure to don’t forget reference bit! 
If reference is forgotten, it might take more time to get the money, as Monzo will need to manually move money to your account.
Sending money via Transferwise is a fairly straightforward process, I did it with my mom not so long ago (she was sending me money from Polish bank), we sat on Skype and I walked her through it.